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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)
What exactly was wrong with the improvements I introduced? Not sure if that's the right place to ask the question... 24.215.166.41 ( talk) 23:46, 23 December 2007 (UTC)
I plan on adding a section on the semantics of constructive set theory soon^TM. It will cover realizability and realizability-with-truth. In particular, this will provide a very rough proof sketch of the disjunction, numerical existence, and church-thesis properties for CZF. I won't include the category theory stuff (I think based on sheafs?) because I'm not actually familiar with it.
Just posting this in case anyone has any comments or objections. TheKing44 ( talk) 13:24, 4 June 2024 (UTC)
![]() | This article is rated Start-class on Wikipedia's
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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)
What exactly was wrong with the improvements I introduced? Not sure if that's the right place to ask the question... 24.215.166.41 ( talk) 23:46, 23 December 2007 (UTC)
I plan on adding a section on the semantics of constructive set theory soon^TM. It will cover realizability and realizability-with-truth. In particular, this will provide a very rough proof sketch of the disjunction, numerical existence, and church-thesis properties for CZF. I won't include the category theory stuff (I think based on sheafs?) because I'm not actually familiar with it.
Just posting this in case anyone has any comments or objections. TheKing44 ( talk) 13:24, 4 June 2024 (UTC)