Ultrafilters and types on models of arithmetic

DOI10.1016/0168-0072(84)90027-7zbMath0565.03014OpenAlexW1965442101MaRDI QIDQ1058509

Laurence Kirby

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)90027-7

zbMATH Keywords

typespartition propertiesarithmetic comprehensiondefinable ultrafilterfragments of second order arithmetic

Mathematics Subject Classification ID

Nonstandard models of arithmetic (03H15) Models of arithmetic and set theory (03C62)

Related Items (11)

Weakly Definable Types ⋮ Models of arithmetic and categories with finiteness conditions ⋮ Automorphisms of models of arithmetic: a unified view ⋮ Arithmetically saturated models of arithmetic ⋮ CONSERVATIVITY OF ULTRAFILTERS OVER SUBSYSTEMS OF SECOND ORDER ARITHMETIC ⋮ A standard model of Peano arithmetic with no conservative elementary extension ⋮ A note on standard systems and ultrafilters ⋮ Automorphism groups of arithmetically saturated models ⋮ A weakly definable type which is not definable ⋮ On maximal subgroups of the automorphism group of a countable recursively saturated model of PA ⋮ Ultrafilters in reverse mathematics

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• End Extensions, Conservative Extensions, and the Rudin-Frolik Ordering
• A model of peano arithmetic with no elementary end extension
• Remarks on some theorems of Keisler
• Ultrafilters on a countable set
• Ramsey's theorem and recursion theory
• The Rudin-Keisler Ordering of P-Points

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