## Notre Dame Journal of Formal Logic

### Definability of Initial Segments

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 15 December 2003

https://projecteuclid.org/euclid.ndjfl/1071509428

Digital Object Identifier
doi:10.1305/ndjfl/1071509428

Mathematical Reviews number (MathSciNet)
MR2033316

Zentralblatt MATH identifier
1082.03038

#### Citation

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

#### References

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