User loginNavigation 
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  4545 reads

Browse archives
Active forum topics

Recent comments
13 weeks 3 days ago
17 weeks 5 days ago
19 weeks 2 days ago
19 weeks 2 days ago
22 weeks 17 hours ago
26 weeks 5 days ago
26 weeks 5 days ago
27 weeks 1 day ago
27 weeks 1 day ago
29 weeks 6 days ago