On external Scott algebras in nonstandard models of Peano arithmetic
Keyword(s):
AbstractWe 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.
2017 ◽
Vol E100.A
(12)
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pp. 2764-2775
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