Saturation and simple extensions of models of Peano arithmetic

DOI10.1016/0168-0072(84)90008-3zbMath0557.03021OpenAlexW2022298124MaRDI QIDQ762144

Matt Kaufmann, James H. Schmerl

Publication date: 1984

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(84)90008-3

zbMATH Keywords

simple extensioncofinal extensionlofty modelsmodel of arithmeticrecursively saturated modelstall models

Mathematics Subject Classification ID

Nonstandard models of arithmetic (03H15) Models of arithmetic and set theory (03C62) Models with special properties (saturated, rigid, etc.) (03C50)

Related Items

Meager sets on the hyperfinite time line ⋮ Set theoretical analogues of the Barwise-Schlipf theorem ⋮ Remarks on weak notions of saturation in models of Peano arithmetic ⋮ On expandability of models of Peano arithmetic to models of the alternative set theory ⋮ Nonstandard definability ⋮ The Barwise-Schlipf theorem ⋮ Models with the ω-property ⋮ AUTOMORPHISM GROUPS OF COUNTABLE ARITHMETICALLY SATURATED MODELS OF PEANO ARITHMETIC ⋮ Modeling vagueness by nonstandardness ⋮ Extendible Sets in Peano Arithmetic

Cites Work

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• On cofinal extensions of models of arithmetic
• Closure properties of countable non-standard integers
• Saturated models of Peano arithmetic
• A Rather Classless Model
• Models with second order properties II. Trees with no undefined branches
• Ultraproducts which are not saturated

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