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1. • CommentRowNumber1.
   • CommentAuthorTodd_Trimble
   • CommentTimeFeb 15th 2015
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexI added to [[continuum hypothesis]] a description of Easton's theorem, and created a page on [[König’s theorem]]. The latter could stand a number of redirects due to variant spellings.

   I added to continuum hypothesis a description of Easton’s theorem, and created a page on König’s theorem. The latter could stand a number of redirects due to variant spellings.

2. • CommentRowNumber2.
   • CommentAuthorDavidRoberts
   • CommentTimeFeb 15th 2015
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexOoh, I should add stuff about class forcing, I know...

   Ooh, I should add stuff about class forcing, I know…

3. • CommentRowNumber3.
   • CommentAuthorDavidRoberts
   • CommentTimeNov 27th 2016
   • (edited Nov 27th 2016)
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexI added some stuff at [[König's theorem]] around the corollary. It needs much improvement. Including, for instance, a discussion of the structural interpretation using a notion of cofinality adapted to coproducts in categories of sets smaller than a given set.

   I added some stuff at König’s theorem around the corollary. It needs much improvement. Including, for instance, a discussion of the structural interpretation using a notion of cofinality adapted to coproducts in categories of sets smaller than a given set.

4. • CommentRowNumber4.
   • CommentAuthorTim_Porter
   • CommentTimeNov 27th 2016
   • (edited Nov 27th 2016)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexDavid: That link is incorrect. 'Lemma' should be 'theorem'.

   David: That link is incorrect. ’Lemma’ should be ’theorem’.

5. • CommentRowNumber5.
   • CommentAuthorTodd_Trimble
   • CommentTimeNov 27th 2016
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItex(Amusingly, the article even warns: not to be confused with König's lemma! The latter is probably a better known result.)

   (Amusingly, the article even warns: not to be confused with König’s lemma! The latter is probably a better known result.)

6. • CommentRowNumber6.
   • CommentAuthorDavidRoberts
   • CommentTimeNov 27th 2016
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexSorry! Brain wasn't thinking. I've edited.

   Sorry! Brain wasn’t thinking. I’ve edited.

7. • CommentRowNumber7.
   • CommentAuthorDavidRoberts
   • CommentTimeNov 27th 2016
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexAn interesting thing I relearned is that in ZF one can have a partition of an uncountable set into just two strictly smaller subsets. I think I'm coming to think of König's corollary (yes, meant that one) as a kind of rigidity result about well-orderable sets with well-orderable powerset. Something analogous to the trichotomy result for the ordering of cardinals. Of course, the big question in my mind is whether any version of the corollary forces well-orderability, where by any version I mean for a sensible definition of cofinality in the absence of AC.

   An interesting thing I relearned is that in ZF one can have a partition of an uncountable set into just two strictly smaller subsets. I think I’m coming to think of König’s corollary (yes, meant that one) as a kind of rigidity result about well-orderable sets with well-orderable powerset. Something analogous to the trichotomy result for the ordering of cardinals. Of course, the big question in my mind is whether any version of the corollary forces well-orderability, where by any version I mean for a sensible definition of cofinality in the absence of AC.