Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 43, Issue 3 (1978), 563-567.
A Model of Peano Arithmetic with no Elementary End Extension
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.
J. Symbolic Logic, Volume 43, Issue 3 (1978), 563-567.
First available in Project Euclid: 6 July 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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