Definability of Initial Segments
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Notre Dame Journal of Formal Logic

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
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

References

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