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Jul 1, 2015 at 21:34 comment added David Roberts Something like constructivism plus a hint of finitism, possibly with predicative leanings. Much more restrictive than would allow arbitrary (sub)sequences.
Jul 1, 2015 at 14:59 comment added Timothy Chow @DavidRoberts : I'm curious as to what you mean by "strict logical hygiene." However, MO is probably not the right forum for having a discussion about that.
Jun 30, 2015 at 23:30 comment added David Roberts Hmm, that's less satisfying than I thought. In particular, as people have pointed out (on tea.mathoverflow for instance) assuming the the mere (in the technical, HoTT, sense) existence of some Cauchy subsequence of an arbitrary sequence, let alone its consistency, is more than someone wanting strict logical hygiene may be willing to admit. Thanks for disabusing me of this misunderstanding :-)
Jun 30, 2015 at 21:13 history edited Timothy Chow CC BY-SA 3.0
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Jun 30, 2015 at 15:20 history answered Timothy Chow CC BY-SA 3.0