Remarks on weak notions of saturation in models of Peano arithmetic

DOI10.2307/2273867zbMath0619.03027OpenAlexW1992833344MaRDI QIDQ3755444

Matt Kaufmann, James H. Schmerl

Publication date: 1987

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2273867

zbMATH Keywords

recursively saturatedminimal modelscountable modelsmodels of Peano arithmeticsaturated modeldiagonal methodsstandard cutrecursively definable

Mathematics Subject Classification ID

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

Related Items

Models of expansions of \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathbb N}$\end{document} with no end extensions ⋮ Definability of initial segments ⋮ The Barwise-Schlipf theorem ⋮ Models with the ω-property ⋮ Set theoretic properties of Loeb measure ⋮ Some highly saturated models of Peano arithmetic ⋮ Decoding in the automorphism group of a recursively saturated model of arithmetic

Cites Work

• Saturation and simple extensions of models of Peano arithmetic
• Construction of Satisfaction Classes for Nonstandard Models
• Full Satisfaction Classes and Recursive Saturation
• Reflection Principles and their Use for Establishing the Complexity of Axiomatic Systems