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1. • CommentRowNumber1.
   • CommentAuthorspitters
   • CommentTimeAug 2nd 2014
   • (edited Aug 2nd 2014)
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   Author: spitters
   Format: MarkdownItexOn the page [[countable choice]] there seemed to be an unsubstantiated claim that weak countable choice proves that the Cauchy and the Dedekind reals coincide. I have cleaned it up a bit. It's not perfect yet.

   On the page countable choice there seemed to be an unsubstantiated claim that weak countable choice proves that the Cauchy and the Dedekind reals coincide. I have cleaned it up a bit. It’s not perfect yet.

2. • CommentRowNumber2.
   • CommentAuthorTobyBartels
   • CommentTimeAug 2nd 2014
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   Author: TobyBartels
   Format: MarkdownItexI probably put it there through mixing up $AC_{00}$ and $WCC$ in my mind (as both weak forms of $CC$), helped because $EM$ also proves this result. But you don\'t need $DC$ to give every (located Dedekind) real number a Cauchy sequence, even with specified modulus. $CC$ is sufficient, because each approximation will automatically be close enough to all of the others if you just make them all twice as precise as would at first seem necessary. I think that $AC_{00}$ is enough, but I can\'t remember why; it\'s probably in Troelstra & van Dalen.

   I probably put it there through mixing up $AC_{00}$ and $WCC$ in my mind (as both weak forms of $CC$), helped because $EM$ also proves this result.

   But you don't need $DC$ to give every (located Dedekind) real number a Cauchy sequence, even with specified modulus. $CC$ is sufficient, because each approximation will automatically be close enough to all of the others if you just make them all twice as precise as would at first seem necessary.

   I think that $AC_{00}$ is enough, but I can't remember why; it's probably in Troelstra & van Dalen.

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeJun 13th 2017
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   Author: Mike Shulman
   Format: MarkdownItexI added to [[countable choice]] the following remark by Fred Richman, which is also borne out by my experience: > Countable choice is a blind spot for constructive mathematicians in much the same way as excluded middle is for classical mathematicians.

   I added to countable choice the following remark by Fred Richman, which is also borne out by my experience:

   Countable choice is a blind spot for constructive mathematicians in much the same way as excluded middle is for classical mathematicians.