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Comments.xml
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<?xml version="1.0" encoding="utf-8"?>
<feed xmlns="http://www.w3.org/2005/Atom">
<title>Booles' Rings -- Comments</title>
<link>http://boolesrings.org/</link>
<updated>2020-09-20T10:45:24Z</updated>
<author>
<name>Booles' Rings</name>
<email>[email protected]</email>
<uri>http://boolesrings.org</uri>
</author>
<link rel="alternate" href="http://boolesrings.org/"/>
<subtitle>Researchers. Connecting.</subtitle>
<logo>http://boolesrings.org/favicon.gif</logo>
<rights>No copyright asserted over individual posts; see original posts for copyright and/or licensing.</rights>
<generator>Feed for Node.js</generator>
<entry>
<title type="html"><![CDATA[Comment on Transfinite Nim by Paul]]></title>
<id>http://jdh.hamkins.org/transfinite-nim/#comment-10945</id>
<link href="http://jdh.hamkins.org/transfinite-nim/#comment-10945">
</link>
<updated>2020-09-19T00:46:21Z</updated>
<summary type="html"><![CDATA[<p>Just finding this post now. Transfinite nim is such a cool problem! Thanks!</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Fake Reflection by saf]]></title>
<id>http://blog.assafrinot.com/?p=4636#comment-834</id>
<link href="http://blog.assafrinot.com/?p=4636#comment-834">
</link>
<updated>2020-09-18T08:58:26Z</updated>
<summary type="html"><![CDATA[<p>Submitted to <em>Israel Journal of Mathematics</em>, February 2020.<br />
Accepted September 2020.</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on All triangles are isosceles by Hew BG]]></title>
<id>http://jdh.hamkins.org/all-triangles-are-isosceles/#comment-10943</id>
<link href="http://jdh.hamkins.org/all-triangles-are-isosceles/#comment-10943">
</link>
<updated>2020-09-17T18:52:08Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://jdh.hamkins.org/all-triangles-are-isosceles/#comment-8353">Joel David Hamkins</a>.</p>
<p>It is slightly hard to disprove the hypothesis that “all triangles are isosceles” by using a triangle that _actually is_ isosceles. 🙂</p>
<p>I had to disabuse my son of this particular argument.</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Dushnik-Miller for regular cardinals (part 1) by David]]></title>
<id>http://blog.assafrinot.com/?p=588#comment-833</id>
<link href="http://blog.assafrinot.com/?p=588#comment-833">
</link>
<updated>2020-09-16T13:51:23Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://blog.assafrinot.com/?p=588#comment-830">saf</a>.</p>
<p>thanks, that’s a nice counterexample!</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Categorical cardinals, CUNY Set Theory Seminar, June 2020 by Categorical large cardinals and the tension between categoricity and set-theoretic reflection | Joel David Hamkins]]></title>
<id>http://jdh.hamkins.org/categorical-cardinals-cuny-set-theory-seminar-june-2020/#comment-10942</id>
<link href="http://jdh.hamkins.org/categorical-cardinals-cuny-set-theory-seminar-june-2020/#comment-10942">
</link>
<updated>2020-09-16T06:50:06Z</updated>
<summary type="html"><![CDATA[<p>[…] Related talk: Categorical cardinals, CUNY Set Theory Seminar, June 2020 […]</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Joel David Hamkins]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10941</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10941">
</link>
<updated>2020-09-14T13:11:55Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10939">Hanul Jeon</a>.</p>
<p>Yes, that is how I understood your argument in the end, and this is how I have presented it in the revised blog post above (with thanks to you).</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Math for eight-year-olds: graph theory for kids! by Having my younger son work through Graph Theory for Kids by Joel David Hamkins – Mike's Math Page]]></title>
<id>http://jdh.hamkins.org/math-for-eight-year-olds/#comment-10940</id>
<link href="http://jdh.hamkins.org/math-for-eight-year-olds/#comment-10940">
</link>
<updated>2020-09-13T16:59:39Z</updated>
<summary type="html"><![CDATA[<p>[…] a good exercise for him. You can find the pdf for the project on Joel David Hamkins’ website:<a href="http://jdh.hamkins.org/math-for-eight-year-olds/My" rel="nofollow ugc">http://jdh.hamkins.org/math-for-eight-year-olds/My</a> son spent about 20 min working through the project and then we talked through all of the pages. […]</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Hanul Jeon]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10939</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10939">
</link>
<updated>2020-09-12T16:01:40Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10936">Joel David Hamkins</a>.</p>
<p>Sorry for checking your reply lately. My initial statement is somewhat misleading: it should be as “if $\kappa$ is a totally otherworldly and $\lambda$ is a $\Sigma_2$-correct cardinal larger than $\kappa$, then $V_\lambda$ sees $\kappa$ is totally otherworldly.” As you pointed out, this statement itself implies no results about consistency strength.</p>
<p>If $\lambda$ is also worldly, then $V_\lambda$ is a model of ZFC with a totally otherworldly cardinal. You proved that a totally otherworldly cardinal is $\Sigma_2$-correct worldly cardinal, so we have the desired result.</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Joel David Hamkins]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10938</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10938">
</link>
<updated>2020-09-12T07:30:07Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10935">Neil Barton</a>.</p>
<p>For question 1, I guess you mean downward absolute to transitive inner models? If so, the answer is negative, and I think it is a little easier even than in the worldly case. Suppose $\kappa$ is otherworldly to $\lambda$. This is preserved by the forcing of the GCH, so we may assume GCH. Now force violations to the GCH with Easton forcing at every successor. This also preserves otherworldliness. But if we stop this latter forcing at $\kappa$, then this would be an inner model where $\kappa$ is no longer otherworldly, since the GCH holds above $\kappa$ but fails unboundedly often below. </p>
<p>(I made a few edits to this comment.)</p>
<p>For question 2, I agree.</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Climb into Cantor's attic by JM]]></title>
<id>http://jdh.hamkins.org/climb-into-cantors-attic/#comment-10937</id>
<link href="http://jdh.hamkins.org/climb-into-cantors-attic/#comment-10937">
</link>
<updated>2020-09-12T07:19:03Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://jdh.hamkins.org/climb-into-cantors-attic/#comment-10788">Joel David Hamkins</a>.</p>
<p>Aw 🙁 that’s sad to hear.</p>
<p>If anyone’s looking for a static archive, most (all?) of the site seems to be on the Wayback Machine, and the MathJax rendering works: <a href="http://web.archive.org/web/20191104130451/http://cantorsattic.info:80/Cantor%27s_Attic" rel="nofollow ugc">http://web.archive.org/web/20191104130451/http://cantorsattic.info:80/Cantor%27s_Attic</a></p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Joel David Hamkins]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10936</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10936">
</link>
<updated>2020-09-11T22:30:51Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10933">Joel David Hamkins</a>.</p>
<p>Oh, I see now. The Sigma_2 correct cardinal you intend to use is the other totally otherworldly cardinal. This seems to work perfectly and it resolves my issue. Thanks! I’ll update the post tomorrow.</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Neil Barton]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10935</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10935">
</link>
<updated>2020-09-11T22:13:12Z</updated>
<summary type="html"><![CDATA[<p>Two questions/observations:</p>
<p>1. Are otherworldly cardinals downward absolute (we know that worldlies, in general, are not)? </p>
<p>2. We always knew that strength and size didn’t go hand in hand (e.g. strong vs. superstrong cardinals). But this is really crazy how big the least totally otherworldly is in the presence of other large cardinals. I guess then we then have “there exists a measurable/huge/whatever and a totally otherworldly” is stronger than “there exists a measurable/huge/whatever and an inaccessible” (since in the latter, the inaccessible is redundant).</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Asaf Karagila]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10934</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10934">
</link>
<updated>2020-09-11T21:26:02Z</updated>
<summary type="html"><![CDATA[<p>I guess the name “elementary cardinal” was taken…</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Joel David Hamkins]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10933</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10933">
</link>
<updated>2020-09-11T20:12:32Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10932">Joel David Hamkins</a>.</p>
<p>Since ZFC proves that the $\Sigma_2$-correct cardinals are unbounded, we cannot expect to prove in ZFC that if there is an totally otherworldly cardinal with a $\Sigma_2$-correct cardinal above, then Con(totally otherworldly), since this would violate the incompleteness theorem.</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Joel David Hamkins]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10932</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10932">
</link>
<updated>2020-09-11T20:10:28Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10931">Hanul Jeon</a>.</p>
<p>Your comment was garbled a little, and I tried to edit it, but now I have become confused about your argument; perhaps I have made a mistake with editing—I apologize. We don’t know that $V_\lambda$ is worldly, so how does your conclusion work?</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The otherwordly cardinals by Hanul Jeon]]></title>
<id>http://jdh.hamkins.org/otherwordly-cardinals/#comment-10931</id>
<link href="http://jdh.hamkins.org/otherwordly-cardinals/#comment-10931">
</link>
<updated>2020-09-11T18:54:37Z</updated>
<summary type="html"><![CDATA[<p>I think the existence of a $\Sigma_2$-correct cardinal above a totally otherworldly cardinal implies the consistency of the existence of a totally otherworldly.</p>
<p>Let $\kappa$ be a totally otherworldly cardinal and $\lambda>\kappa$ be a $\Sigma_2$-correct cardinal. Take $\alpha<\lambda$ and $\beta>\alpha$ such that $V_\kappa\prec V_\beta$. </p>
<p>Since $V_{\beta+1}\models (\beta>\alpha\land V_\kappa\prec V_\beta)$, we have $V_{\beta+1}\models \exists\xi (\xi>\alpha\land V_\kappa\prec V_\xi)$.<br />
By $\Sigma_2$-correctness of $\lambda$, there is $\gamma<\lambda$ with $\gamma>\alpha\land V_\kappa\prec V_\gamma)$. Hence $V_\lambda\models (\exists\xi (\xi>\alpha\land V_\kappa\prec V_\xi)$. Since $\alpha$ is arbitrary, $V_\lambda$ thinks $\kappa$ is totally otherworldly.</p>
<p>Since every totally otherworldly cardinal is $\Sigma_2$-correct, the existence of two totally otherworldly cardinals implies the consistency of the existence of a totally otherworldly cardinal.</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Local properties in set theory by The otherwordly cardinals | Joel David Hamkins]]></title>
<id>http://jdh.hamkins.org/local-properties-in-set-theory/#comment-10930</id>
<link href="http://jdh.hamkins.org/local-properties-in-set-theory/#comment-10930">
</link>
<updated>2020-09-11T15:12:29Z</updated>
<summary type="html"><![CDATA[<p>[…] an assertion of the form $existseta V_etamodelspsi$ (for more information, see my post about Local properties in set theory). Thus, every true $Sigma_2$ assertion is revealed inside any sufficiently large $V_lambda$, and […]</p>]]></summary>
<author>
<name>Comments for Joel David Hamkins</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Dushnik-Miller for regular cardinals (part 1) by saf]]></title>
<id>http://blog.assafrinot.com/?p=588#comment-830</id>
<link href="http://blog.assafrinot.com/?p=588#comment-830">
</link>
<updated>2020-09-04T14:10:54Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://blog.assafrinot.com/?p=588#comment-818">David</a>.</p>
<p>Hi David! Let us demonstrate that $\omega_2\nrightarrow(\omega_2,\text{closed}(\omega_1+1))^2$.<br />
For every limit ordinal $\beta<\omega_2$, fix a club $D_\beta$ in $\beta$ of order-type $cf(\beta)$,<br />
and then pick a coloring $c:[\omega_2]^2\rightarrow\{0,1\}$ such that, for every limit ordinal $\beta<\omega_2$, and every $\alpha<\beta$, $c(\alpha,\beta)=0$ iff $\alpha\in D_\beta$.
<li>$\blacktriangleright$ For every cofinal subset $S$ of $\omega_2$, we may find some $\beta\in S$ such that $S\cap\beta$ has order-type $>\omega_1$, and hence, there is $\alpha\in S\setminus D_\beta$, so that $c(\alpha,\beta)=1$.</li>
<li>$\blacktriangleright$ For every club $C$ in an ordinal $\beta$ of uncountable cofinality, we may find $\alpha\in C\cap D_\beta$, so that $c(\alpha,\beta)=0$.</li>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Dushnik-Miller for regular cardinals (part 1) by David]]></title>
<id>http://blog.assafrinot.com/?p=588#comment-818</id>
<link href="http://blog.assafrinot.com/?p=588#comment-818">
</link>
<updated>2020-07-27T13:09:11Z</updated>
<summary type="html"><![CDATA[<p>As to the result of Erdos and Rado assuming CH it holds that: $\omega_2 \rightarrow (\omega_2, \omega_1 + 1)^2$, also the 0-homogeneous set can be made stationary [Handbook of Set Theory, ch. 2., 3.11]. Can it be strengthened to also require the 1-homogeneous set to be closed, i.e. a club subset of some uncountable ordinal $< \omega_2$ ?</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on A Microscopic approach to Souslin-tree constructions. Part I by Ari B.]]></title>
<id>http://blog.assafrinot.com/?p=4059#comment-814</id>
<link href="http://blog.assafrinot.com/?p=4059#comment-814">
</link>
<updated>2020-06-24T17:52:08Z</updated>
<summary type="html"><![CDATA[<p>Best to start reading with Part II, linked at “Further Reading” above, which is comprehensive, up-to-date, and accessible to beginners.</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on A Microscopic approach to Souslin-tree constructions. Part II by saf]]></title>
<id>http://blog.assafrinot.com/?p=4631#comment-811</id>
<link href="http://blog.assafrinot.com/?p=4631#comment-811">
</link>
<updated>2020-06-18T12:15:28Z</updated>
<summary type="html"><![CDATA[<p>Submitted to Annals of Pure and Applied Logic, January 2020.<br />
Accepted, June 2020.</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Knaster and friends II: The C-sequence number by saf]]></title>
<id>http://blog.assafrinot.com/?p=4607#comment-806</id>
<link href="http://blog.assafrinot.com/?p=4607#comment-806">
</link>
<updated>2020-06-07T13:37:55Z</updated>
<summary type="html"><![CDATA[<p>Submitted to J. Math. Logic, October 2019.<br />
Accepted, June 2020.</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Sigma-Prikry forcing I: The Axioms by saf]]></title>
<id>http://blog.assafrinot.com/?p=4596#comment-803</id>
<link href="http://blog.assafrinot.com/?p=4596#comment-803">
</link>
<updated>2020-05-19T00:13:04Z</updated>
<summary type="html"><![CDATA[<p>Submitted to Canadian Journal of Mathematics, September 2019.<br />
Accepted, May 2020.</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Inclusion modulo nonstationary by saf]]></title>
<id>http://blog.assafrinot.com/?p=4582#comment-802</id>
<link href="http://blog.assafrinot.com/?p=4582#comment-802">
</link>
<updated>2020-05-19T00:09:57Z</updated>
<summary type="html"><![CDATA[<p>Submitted to Monatshefte für Mathematik, June 2019.<br />
Accepted, May 2020.</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Knaster and friends I: Closed colorings and precalibers by saf]]></title>
<id>http://blog.assafrinot.com/?p=4530#comment-744</id>
<link href="http://blog.assafrinot.com/?p=4530#comment-744">
</link>
<updated>2019-11-02T11:05:13Z</updated>
<summary type="html"><![CDATA[<p>Correction of two typos:<br />
1. At the opening of the proof of Theorem 4.23, where it says “By Corollary 4.19”, it should have been “By Corollary 4.12”.<br />
2. Later in the proof of Theorem 4.23, where defining the ordinal $\Lambda$, the function $\lambda_2^k$ should have been $\lambda_2$ (the extra superscript is only relevant to the proof of Case 2 of Theorem 4.21, and is redundant here).</p>]]></summary>
<author>
<name>Comments for Assaf Rinot</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Enjoying new business job by Joel David Hamkins]]></title>
<id>http://normanspace.org/2016/11/11/enjoying-new-business-job/#comment-43</id>
<link href="http://normanspace.org/2016/11/11/enjoying-new-business-job/#comment-43">
</link>
<updated>2016-11-13T15:06:26Z</updated>
<summary type="html"><![CDATA[<p>Glad to hear it is working out well, Norman. We miss you in New York — hope to see you again some time. I think that infinite chess idea may work out!</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Resigning from LaGuardia by Ali Sadegh Daghighi]]></title>
<id>http://normanspace.org/2016/08/02/resigning-from-laguardia/#comment-42</id>
<link href="http://normanspace.org/2016/08/02/resigning-from-laguardia/#comment-42">
</link>
<updated>2016-08-09T18:26:34Z</updated>
<summary type="html"><![CDATA[<p>Wish you the bests in your life and career, Norman! 🙂</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Resigning from LaGuardia by Joel David Hamkins]]></title>
<id>http://normanspace.org/2016/08/02/resigning-from-laguardia/#comment-41</id>
<link href="http://normanspace.org/2016/08/02/resigning-from-laguardia/#comment-41">
</link>
<updated>2016-08-07T11:41:29Z</updated>
<summary type="html"><![CDATA[<p>We’ll miss you, Norman! Best of luck for the future.</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Infinite chess by Joel David Hamkins]]></title>
<id>http://normanspace.org/2015/02/25/infinite-chess/#comment-30</id>
<link href="http://normanspace.org/2015/02/25/infinite-chess/#comment-30">
</link>
<updated>2015-03-02T14:29:07Z</updated>
<summary type="html"><![CDATA[<p>I fairly optimistic about it also!</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Filter quantifiers by Carl Mummert]]></title>
<id>http://m6c.org/w/2014/11/filter-quantifiers/#comment-69528</id>
<link href="http://m6c.org/w/2014/11/filter-quantifiers/#comment-69528">
</link>
<updated>2014-12-17T13:02:31Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://m6c.org/w/2014/11/filter-quantifiers/#comment-69449">Peter</a>.</p>
<p>Thanks – I’ll look up some of those. I hope to go back eventually and expand the note some.</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Filter quantifiers by Carl Mummert]]></title>
<id>http://m6c.org/w/2014/11/filter-quantifiers/#comment-69527</id>
<link href="http://m6c.org/w/2014/11/filter-quantifiers/#comment-69527">
</link>
<updated>2014-12-17T13:00:38Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://m6c.org/w/2014/11/filter-quantifiers/#comment-62041">Dave L. Renfro</a>.</p>
<p>Thanks. I’ll need to pull those books by Thomson to see what’s in there. The surprising thing to me is that this material is apparently not in any introductory logic textbooks.</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Filter quantifiers by Peter]]></title>
<id>http://m6c.org/w/2014/11/filter-quantifiers/#comment-69449</id>
<link href="http://m6c.org/w/2014/11/filter-quantifiers/#comment-69449">
</link>
<updated>2014-12-17T08:13:30Z</updated>
<summary type="html"><![CDATA[<p>Not directly related, but Andreas has written lots of stuff on filters and quantifiers, going all the way back to his thesis. His union ultrafilters paper from 1987 has a few comments on quantifiers, his 1993 introductory paper definitely has some treatment (and in my thesis, the definition of idempotent filters comes down to his supervision). </p>
<p>The book by Hindman&Strauss has a section on filters and compactifications in a later chapter — that might be suitable for 2).</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Filter quantifiers by Dave L. Renfro]]></title>
<id>http://m6c.org/w/2014/11/filter-quantifiers/#comment-62041</id>
<link href="http://m6c.org/w/2014/11/filter-quantifiers/#comment-62041">
</link>
<updated>2014-12-01T22:09:15Z</updated>
<summary type="html"><![CDATA[<p>What follows mostly repeats a comment I just made on your 1 December 2014 math StackExchange question about this issue. I’m putting my comment here for anyone who might be interested but doesn’t visit that site.</p>
<p>Possibly relevant is my October 2004 sci.math post “Generalized Quantifiers” (URLs below). FYI, the Math Forum version has a lot of strange formatting errors. See also Brian Thomson’s 1985 book “Real Functions”, and see Thomson’s earlier 2-part survey Derivation bases on the real line (which contain examples and side-detours not in his book).</p>
<p>google sci.math URL:<br />
<a href="https://groups.google.com/forum/#!msg/sci.math/rhZEhXynVLQ/MI0MJ0ZQIvoJ" rel="nofollow ugc">https://groups.google.com/forum/#!msg/sci.math/rhZEhXynVLQ/MI0MJ0ZQIvoJ</a></p>
<p>Math Forum sci.math URL:<br />
<a href="http://mathforum.org/kb/message.jspa?messageID=3556191" rel="nofollow ugc">http://mathforum.org/kb/message.jspa?messageID=3556191</a></p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Got a tenure-track position at LaGuardia Community College by Joel David Hamkins]]></title>
<id>http://normanspace.org/2014/06/12/got-a-tenure-track-position-at-laguardia-community-college/#comment-29</id>
<link href="http://normanspace.org/2014/06/12/got-a-tenure-track-position-at-laguardia-community-college/#comment-29">
</link>
<updated>2014-06-16T17:32:11Z</updated>
<summary type="html"><![CDATA[<p>We’ll be glad to have you back in New York, Norman!</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Got a tenure-track position at LaGuardia Community College by Norman Lewis Perlmutter]]></title>
<id>http://normanspace.org/2014/06/12/got-a-tenure-track-position-at-laguardia-community-college/#comment-28</id>
<link href="http://normanspace.org/2014/06/12/got-a-tenure-track-position-at-laguardia-community-college/#comment-28">
</link>
<updated>2014-06-14T22:42:24Z</updated>
<summary type="html"><![CDATA[<p>Thanks, Francois. I think that’s good advice.</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Got a tenure-track position at LaGuardia Community College by François G. Dorais]]></title>
<id>http://normanspace.org/2014/06/12/got-a-tenure-track-position-at-laguardia-community-college/#comment-27</id>
<link href="http://normanspace.org/2014/06/12/got-a-tenure-track-position-at-laguardia-community-college/#comment-27">
</link>
<updated>2014-06-13T23:21:52Z</updated>
<summary type="html"><![CDATA[<p>Congratulations Norman!!!</p>
<p>Regarding <q>Moving around every few years for postdocs would be exhausting</q>, I wholeheartedly agree! Every such decision has pros and cons. They are usually not obvious at the outset. Moreover, they change over time. The lesson I learned though my own course is that every decision is right, at least at the time you make it, and there is never any point regretting it later on… Just keep on doing what you do best all the time!</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Got a tenure-track position at LaGuardia Community College by Asaf Karagila]]></title>
<id>http://normanspace.org/2014/06/12/got-a-tenure-track-position-at-laguardia-community-college/#comment-26</id>
<link href="http://normanspace.org/2014/06/12/got-a-tenure-track-position-at-laguardia-community-college/#comment-26">
</link>
<updated>2014-06-13T00:38:29Z</updated>
<summary type="html"><![CDATA[<p>Congratulations!</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on This was freaky by Joel David Hamkins]]></title>
<id>http://normanspace.org/2014/04/01/this-was-freaky/#comment-25</id>
<link href="http://normanspace.org/2014/04/01/this-was-freaky/#comment-25">
</link>
<updated>2014-04-02T01:27:23Z</updated>
<summary type="html"><![CDATA[<p>I once gave a talk at a gathering of high school students competing in a math olympics contest, and the main thesis I wanted to prove to them was: It is very likely that rare events occur. We discussed the odds of a particular pattern of outcome when flipping a coin six times. Any particular pattern, we all agreed, was remote, occurring with probability 1/64. And then on the stage I actually flipped the coin six times. But it was manifest that we would get *some* pattern, so I had proved my point, that it was very likely that a rare event occurs. </p>
<p>We went on to look at the paradoxical situations that arise when someone gets a positive test result for a rare disease. Should they be worried? If the test is 99% accurate, but the disease occurs in say, 1 in million, then a positive result is not so worrisome: in million people, there will be about 1 true positive result, and about 10,000 false positives, since 1% of a million is 10,000. So the odds that you’ve actually got the disease, given that you tested positive, is 1 in 10,000. </p>
<p>But your situation is completely different! It would be as though we had calculated the odds of getting HHHTTT, and then when I actually flipped the coin on stage, i actually got the same pattern HHHTTT. Totally weird! And very unlikely. But you know, if it wasn’t that, it would have been some other totally unlikely thing, like getting all green lights, or all red lights, or getting the serial number 123456 on your receipt at Starbucks.</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Strange humor by Erin Carmody]]></title>
<id>http://normanspace.org/2014/02/27/teaching-evaluations/#comment-24</id>
<link href="http://normanspace.org/2014/02/27/teaching-evaluations/#comment-24">
</link>
<updated>2014-03-01T03:21:37Z</updated>
<summary type="html"><![CDATA[<p>That”s funny Norm. I bet the students enjoy your class.</p>]]></summary>
<author>
<name>Comments for Norman Lewis Perlmutter</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Quiz on public peer review by Carl Mummert]]></title>
<id>http://m6c.org/w/2012/04/296/#comment-13192</id>
<link href="http://m6c.org/w/2012/04/296/#comment-13192">
</link>
<updated>2013-12-11T17:03:30Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://m6c.org/w/2012/04/296/#comment-13184">Matthew B</a>.</p>
<p>Thanks for the comment. I do want to point out that I have the copyright to all my papers on the arXiv. I don’t know whether any papers there are in the public domain, but the default license grants the arXiv just enough rights to publish the paper, while reserving all other rights for the author. The arXiv, for mathematics, does resolve many issues with peer review, from the delay in dissemination to the cost of paywalls. This, and the practice of speaking about results immediately, long before formal publication, makes the peer review system in mathematics essentially a secondary mechanism for establishing credentials, rather than the primary mechanism for publishing. Unfortunately, there are many scientific disciplines that have nothing analogous to the arXiv, and which do not tend to publicize results before formal publication. The situation in those areas is very different.</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Quiz on public peer review by Matthew B]]></title>
<id>http://m6c.org/w/2012/04/296/#comment-13184</id>
<link href="http://m6c.org/w/2012/04/296/#comment-13184">
</link>
<updated>2013-12-11T15:02:15Z</updated>
<summary type="html"><![CDATA[<p>I think there is no doubt the peer-review process is corrupted: I’m sure I am not the only one who has seen reviewers with motives/agendas reject work worthy of being published. I’ve always thought the problem WAS peer-review, so why not just abolish it? Personally, I think ArXiv is the solution to this problem. It is free, there is no copyright, and people can make up their own minds as to whether or not they think it is good.</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Talk on Reverse Mathematics and the Modal Logic of Reverse Mathematics by Joel David Hamkins]]></title>
<id>http://m6c.org/w/2013/11/talk-on-reverse-mathematics-and-the-modal-logic-of-reverse-mathematics/#comment-12641</id>
<link href="http://m6c.org/w/2013/11/talk-on-reverse-mathematics-and-the-modal-logic-of-reverse-mathematics/#comment-12641">
</link>
<updated>2013-11-26T01:57:04Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://m6c.org/w/2013/11/talk-on-reverse-mathematics-and-the-modal-logic-of-reverse-mathematics/#comment-12639">Carl Mummert</a>.</p>
<p>I saw that you’ll be speaking on this at the JMM (<a href="http://jointmathematicsmeetings.org/amsmtgs/2160_abstracts/1096-03-1603.pdf" rel="nofollow ugc">http://jointmathematicsmeetings.org/amsmtgs/2160_abstracts/1096-03-1603.pdf</a>), and I shall look forward to it.</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Talk on Reverse Mathematics and the Modal Logic of Reverse Mathematics by Carl Mummert]]></title>
<id>http://m6c.org/w/2013/11/talk-on-reverse-mathematics-and-the-modal-logic-of-reverse-mathematics/#comment-12639</id>
<link href="http://m6c.org/w/2013/11/talk-on-reverse-mathematics-and-the-modal-logic-of-reverse-mathematics/#comment-12639">
</link>
<updated>2013-11-26T00:55:52Z</updated>
<summary type="html"><![CDATA[<p>Thanks, Joel.</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on Talk on Reverse Mathematics and the Modal Logic of Reverse Mathematics by Joel David Hamkins]]></title>
<id>http://m6c.org/w/2013/11/talk-on-reverse-mathematics-and-the-modal-logic-of-reverse-mathematics/#comment-12637</id>
<link href="http://m6c.org/w/2013/11/talk-on-reverse-mathematics-and-the-modal-logic-of-reverse-mathematics/#comment-12637">
</link>
<updated>2013-11-26T00:36:01Z</updated>
<summary type="html"><![CDATA[<p>Carl, this is really very nice, and I like it a lot.</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
<entry>
<title type="html"><![CDATA[Comment on The logic of Reverse Mathematics by Carl Mummert]]></title>
<id>http://m6c.org/w/2011/12/logic-of-reverse-mathematics/#comment-11065</id>
<link href="http://m6c.org/w/2011/12/logic-of-reverse-mathematics/#comment-11065">
</link>
<updated>2013-09-03T11:41:29Z</updated>
<summary type="html"><![CDATA[<p>In reply to <a href="http://m6c.org/w/2011/12/logic-of-reverse-mathematics/#comment-11045">Jason Rute</a>.</p>
<p>Thanks – I updated the post.</p>]]></summary>
<author>
<name>Comments for Carl Mummert</name>
</author>
</entry>
</feed>