Models with the ω-property
Journal of Symbolic Logic 54 (1):177-189 (1989)
Abstract
A model M of PA has the omega-property if it has a subset of order type omega that is coded in an elementary end extension of M. All countable recursively saturated models have the omega-property, but there are also models with the omega-property that are not recursively saturated. The papers is devoted to the study of structural properties of such models.Author's Profile
DOI
10.2307/2275023
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Citations of this work
Automorphisms of recursively saturated models of arithmetic.Richard Kaye, Roman Kossak & Henryk Kotlarski - 1991 - Annals of Pure and Applied Logic 55 (1):67-99.
Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.
On Cofinal Submodels and Elementary Interstices.Roman Kossak & James H. Schmerl - 2012 - Notre Dame Journal of Formal Logic 53 (3):267-287.
References found in this work
Saturation and simple extensions of models of peano arithmetic.Matt Kaufmann & James H. Schmerl - 1984 - Annals of Pure and Applied Logic 27 (2):109-136.
A note on initial segment constructions in recursively saturated models of arithmetic.C. Smoryński - 1982 - Notre Dame Journal of Formal Logic 23 (4):393-408.
Recursively saturated $\omega_1$-like models of arithmetic.Roman Kossak - 1985 - Notre Dame Journal of Formal Logic 26 (4):413-422.
