Definability of Initial Segments

Saharon Shelah; Akito Tsuboi

doi:10.1305/ndjfl/1071509428

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Home > Journals > Notre Dame J. Formal Logic > Volume 43 > Issue 2 > Article

2002 Definability of Initial Segments

Saharon Shelah, Akito Tsuboi

Notre Dame J. Formal Logic 43(2): 65-73 (2002). DOI: 10.1305/ndjfl/1071509428

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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.

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Saharon Shelah. Akito Tsuboi. "Definability of Initial Segments." Notre Dame J. Formal Logic 43 (2) 65 - 73, 2002. https://doi.org/10.1305/ndjfl/1071509428