Answer by Paul Taylor for Ordinals in constructive mathematics ? (references)
The first response to any question about "the" ordinals is what you want to do with them. Regrettably, that is most often to find the fixed point of some construction within some already-known object,...
View ArticleAnswer by Toby Bartels for Ordinals in constructive mathematics ? (references)
If you want proof by induction, then you do want to use well-ordered sets, but you need the correct definition of ‘well-ordered’. Of course we can't require that any non-empty subset have a minimal...
View ArticleAnswer by Bas Spitters for Ordinals in constructive mathematics ? (references)
Perhaps the literature on W-types is what you are looking for? This is well-developed categorically and gives a good theory of inductive types.If you are looking explicitly for ordinals, there's a...
View ArticleOrdinals in constructive mathematics ? (references)
I'm looking for references presenting a constructive treatment of the theory of ordinals. By constructive I mean valid in the internal logic of a topos (so no axiom of choice and no law of excluded...
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