Questions tagged [transfinite-induction]
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Is $\in$-induction provable in first order Zermelo set theory?
Are there models of first order Zermelo set theory (axiomatized by: Extensionaity, Foundation, empty set, pairing, set union, power, Separation, infinity) in which $\in$-induction fail?
I asked this ...
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What is induction up to $\varepsilon_0$?
This is a question asked out of curiosity, and because I can't understand the Wikipedia page.
I have often been told that PA cannot prove the validity of induction up to $\varepsilon_0$, which has ...
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Is there a stronger form of recursion?
I'm wondering if there are any recursion principles more general than the following, first given by Montague, Tarski and Scott (1956):
Let $\mathbb{V}$ be the universe, and $\mathcal{R}$ be a well-...
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Is strengthening Foundation in NBG sufficient to make it prove Con(ZFC)?
Can $\sf NBG$ class theory prove the foundation scheme:
Foundation schema: if $\Phi(X)$ is a formula in which "$X$" occurs free and only free, and in which "$Y$" doesn't occur, ...
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Does Regularity schema imply $\in$-induction when added to first order Zermelo set theory?
That $\in$-induction fails to be a theorem schema of first order Zermelo + Foundation (see here), then it appears that it is more eligible to replace axiom of Regularity (Foundation) by a Regularity ...
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