Comments on: 580 -Some choiceless results (3)
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/
Andrés E. CaicedoTue, 08 Mar 2022 12:52:23 +0000
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By: What is a Cantor-style proof of 2n>nk2^n > n^k? – Math Solution
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-15014
Tue, 08 Mar 2022 12:52:23 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-15014[…] that mathfrak m^2=mathfrak m for all infinite mathfrak m — see the first lemma in section 6, here, where it is also shown that there are explicit bijections f_alpha:alphatoalphatimesalpha for […]
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By: Question about Generalized Continuum Hypothesis [closed] – Math Solution
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-15006
Mon, 07 Mar 2022 16:29:32 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-15006[…] set of finite sequences of elements of X. This was proved by Halbeisen and Shelah, see for example this blog post of […]
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By: 580 -Some choiceless results | A kind of library
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-9495
Wed, 27 Feb 2019 03:40:29 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-9495[…] (Dec. 3, 2009). The pdf file still contains an error that was pointed out to me recently. In the third lecture on choiceless results, the correct argument is […]
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By: Yu Mika
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-9403
Sat, 16 Feb 2019 13:06:22 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-9403In the proof for the lemma for Halbeisen-Shelah why you have that both α and β has the same sequence in the exponential part? Also in the end of the proof for Halbeisen-Shelah what is the canonical injective from αω to αα?
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By: 580 -Some choiceless results (5) « A kind of library
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-3903
Tue, 01 Jan 2013 23:13:29 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-3903[…] where the strict inequality is Specker’s lemma, shown on lecture 3, section 5. By , we have . (In particular, is […]
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By: 580 -II. Cardinal arithmetic « A kind of library
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-3901
Tue, 01 Jan 2013 23:06:19 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-3901[…] is infinite, and the fact that and have the same size, for any infinite ordinal , as shown on lecture 3, lemma in section […]
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By: 580- Specker trees « A kind of library
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-3383
Mon, 27 Aug 2012 21:11:17 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-3383[…] set of all ordinals that inject into , so is the first ordinal that cannot inject. Sierpiński proved that and therefore . This observation gives us immediately that the Specker tree of any set is […]
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By: 580- Specker trees « Teaching blog
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-3056
Sat, 12 Feb 2011 03:06:23 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-3056[…] set of all ordinals that inject into , so is the first ordinal that cannot inject. Sierpiński proved that and therefore . This observation gives us immediately that the Specker tree of any set is […]
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By: andrescaicedo
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-3054
Fri, 04 Dec 2009 01:34:27 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-3054Lorenzo Traldi noticed that there was an error in the proof that there is a canonical bijection between and for all infinite ordinals I have replaced the flawed argument with a correct one.
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By: 580 -Some choiceless results « Teaching blog
https://andrescaicedo.wordpress.com/2009/01/27/580-some-choiceless-results-3/#comment-3055
Fri, 04 Dec 2009 00:37:35 +0000http://caicedoteaching.wordpress.com/?p=1117#comment-3055[…] (Dec. 3, 2009). The pdf file still contains an error that was pointed out to me recently. In the third lecture on choiceless results, the correct argument is […]
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