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On external Scott algebras in nonstandard models of Peano arithmetic

Published online by Cambridge University Press:  12 March 2014

Vladimir Kanovei*
Affiliation:
Department of Mathematics (Vychislitelnaya), Moscow Transport Engineering Institute, Obraztsova 15, Moscow 101475, Russia, E-mail: kanovei@mech.math.msu.su, kanovei@math.uni-wuppertal.de

Abstract

We prove that a necessary and sufficient condition for a countable set of sets of integers to be equal to the algebra of all sets of integers definable in a nonstandard elementary extension of ω by a formula of the PA language which may include the standardness predicate but does not contain nonstandard parameters, is as follows: is closed under arithmetical definability and contains 0(ω) the set of all (Gödel numbers of) true arithmetical sentences.

Some results related to definability of sets of integers in elementary extensions of ω are included.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1996

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References

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