Disputed

I'm willing to take your word as to Myhill's theories, but it's only equivalent to a one-sorted theory (with additional predicates) if functions are also (equal to) sets, and ℕ is also equal to a set.

Furthermore, in classical set theory, the power set of a set X is equivalent to the set of functions from X to 2. — Arthur Rubin | (talk) 08:04, 7 May 2006 (UTC)[reply]

2^x is not the power set of x. That would be the law of the excluded middle! As for the rest, the "axiom of non-choice" is essentialy the bridge for functions, and the natural numbers can, and I'm sure you knew this, easily be encoded as sets. But yes, I do realise this all needs expansion and citation. -Dan 16:40, 7 May 2006 (UTC)

What is the difference between 2^x and the power set of x in ~~heretical~~ intuitionistic set theory? (And for that matter, what is the difference between "constructive set theory" and intuitionistic set theory?) — Arthur Rubin | (talk) 17:32, 11 May 2006 (UTC)[reply]