Definability of Initial Segments

Definability of Initial Segments

Saharon Shelah and Akito Tsuboi

Source: Notre Dame J. Formal Logic Volume 43, Number 2 (2002), 65-73.

Abstract

In any nonstandard model of Peano arithmetic, the standard part is not first-order definable. But we show that in some model the standard part is definable as the unique solution of a formula $\varphi(P)$ , where P is a unary predicate variable.

Primary Subjects: 03C62, 03H15

Secondary Subjects: 03C55

Keywords: Peano arithmetic; definability; absoluteness

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1071509428
Digital Object Identifier: doi:10.1305/ndjfl/1071509428
Mathematical Reviews number (MathSciNet): MR2033316
Zentralblatt MATH identifier: 02068392

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References

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Mathematical Reviews (MathSciNet): MR88g:03053

Zentralblatt MATH: 0619.03027

JSTOR: links.jstor.org

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Zentralblatt MATH: 0364.02032

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Digital Object Identifier: doi:10.1016/0003-4843(78)90008-6

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Mathematical Reviews (MathSciNet): MR85j:03056

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