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Extreme nonchoosinessAs a mathematician who's quite new to type theory, I have only vaguely internalised the fact that
I tried to recast this in language more familiar to me, and wound up with the statement that the product of all sets is empty. Now, I know that type theories tend (understandably) to be biased more towards constructivist than traditional ZFCbased axiomatisations; but it seems to me that, beyond just saying that we don't assume the Axiom of Choice, this statement is saying that we take that axiom as the definition of ‘false’! Is the rejection of choosiness really so definitive, or am I just skipping over some point (like, say, that some sets are empty, so that including them in the product will naturally make it, too, empty)? By L Spice at 20100203 06:55  LtU Forum  previous forum topic  next forum topic  other blogs  3345 reads

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