Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 49, Number 4 (2008), 345-360.
Automorphisms of Countable Short Recursively Saturated Models of PA
A model of Peano Arithmetic is short recursively saturated if it realizes all its bounded finitely realized recursive types. Short recursively saturated models of are exactly the elementary initial segments of recursively saturated models of . In this paper, we survey and prove results on short recursively saturated models of and their automorphisms. In particular, we investigate a certain subgroup of the automorphism group of such models. This subgroup, denoted , contains all the automorphisms of a countable short recursively saturated model of which can be extended to an automorphism of the countable recursively saturated elementary end extension of the model.
Notre Dame J. Formal Logic, Volume 49, Number 4 (2008), 345-360.
First available in Project Euclid: 17 October 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03C62: Models of arithmetic and set theory [See also 03Hxx]
Shochat, Erez. Automorphisms of Countable Short Recursively Saturated Models of PA. Notre Dame J. Formal Logic 49 (2008), no. 4, 345--360. doi:10.1215/00294527-2008-016. https://projecteuclid.org/euclid.ndjfl/1224257535