Automorphisms of models of arithmetic: a unified view

Annals of Pure and Applied Logic 145 (1):16-36 (2007)

We develop the method of iterated ultrapower representation to provide a unified and perspicuous approach for building automorphisms of countable recursively saturated models of Peano arithmetic . In particular, we use this method to prove Theorem A below, which confirms a long-standing conjecture of James Schmerl.Theorem AIf is a countable recursively saturated model of in which is a strong cut, then for any there is an automorphism j of such that the fixed point set of j is isomorphic to .We also fine-tune a number of classical results. One of our typical results in this direction is Theorem B below, which generalizes a theorem of Kaye–Kossak–Kotlarski .Theorem BSuppose is a countable recursively saturated model of in which is a strong cut. There is a group embedding from into such that for each that is fixed point free, moves every undefinable element of
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DOI 10.1016/j.apal.2006.05.013
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References found in this work BETA

Some Applications of Iterated Ultrapowers in Set Theory.Kenneth Kunen - 1970 - Annals of Pure and Applied Logic 1 (2):179.
Models and Types of Peano's Arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Partition Theorems and Computability Theory.Joseph R. Mileti - 2005 - Bulletin of Symbolic Logic 11 (3):411-427.
Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.

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Citations of this work BETA

Iterated Ultrapowers for the Masses.Ali Enayat, Matt Kaufmann & Zachiri McKenzie - 2018 - Archive for Mathematical Logic 57 (5-6):557-576.

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