Journal of Symbolic Logic

On External Scott Algebras in Nonstandard Models of Peano Arithmetic

Vladimir Kanovei

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.

Abstract

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.

Article information

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

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745016

Mathematical Reviews number (MathSciNet)
MR1394616

Zentralblatt MATH identifier
0859.03034

JSTOR
links.jstor.org

Citation

Kanovei, Vladimir. On External Scott Algebras in Nonstandard Models of Peano Arithmetic. J. Symbolic Logic 61 (1996), no. 2, 586--607. https://projecteuclid.org/euclid.jsl/1183745016


Export citation