Notre Dame Journal of Formal Logic

Definability of Initial Segments

Saharon Shelah and Akito Tsuboi


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

First available in Project Euclid: 15 December 2003

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Zentralblatt MATH identifier

Primary: 03C62: Models of arithmetic and set theory [See also 03Hxx] 03H15: Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05]
Secondary: 03C55: Set-theoretic model theory

Peano arithmetic definability absoluteness


Shelah, Saharon; Tsuboi, Akito. Definability of Initial Segments. Notre Dame J. Formal Logic 43 (2002), no. 2, 65--73. doi:10.1305/ndjfl/1071509428.

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