Journal of Symbolic Logic

A Model of Peano Arithmetic with no Elementary End Extension

George Mills

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Abstract

We construct a model of Peano arithmetic in an uncountable language which has no elementary end extension. This answers a question of Gaifman and contrasts with the well-known theorem of MacDowell and Specker which states that every model of Peano arithmetic in a countable language has an elementary end extension. The construction employs forcing in a nonstandard model.

Article information

Source
J. Symbolic Logic, Volume 43, Issue 3 (1978), 563-567.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183740261

Mathematical Reviews number (MathSciNet)
MR491159

Zentralblatt MATH identifier
0388.03029

JSTOR
links.jstor.org

Citation

Mills, George. A Model of Peano Arithmetic with no Elementary End Extension. J. Symbolic Logic 43 (1978), no. 3, 563--567. https://projecteuclid.org/euclid.jsl/1183740261


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