Journal of Symbolic Logic

On External Scott Algebras in Nonstandard Models of Peano Arithmetic

Vladimir Kanovei

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We prove that a necessary and sufficient condition for a countable set $\mathscr{L}$ of sets of integers to be equal to the algebra of all sets of integers definable in a nonstandard elementary extension of $\omega$ by a formula of the $\mathrm{PA}$ language which may include the standardness predicate but does not contain nonstandard parameters, is as follows: $\mathscr{L}$ is closed under arithmetical definability and contains $0^{(\omega)}$, the set of all (Godel numbers of) true arithmetical sentences. Some results related to definability of sets of integers in elementary extensions of $\omega$ are included.

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J. Symbolic Logic, Volume 61, Issue 2 (1996), 586-607.

First available in Project Euclid: 6 July 2007

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Kanovei, Vladimir. On External Scott Algebras in Nonstandard Models of Peano Arithmetic. J. Symbolic Logic 61 (1996), no. 2, 586--607.

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