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Notre Dame Journal of Formal Logic
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Notre Dame Journal of Formal Logic
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Arithmetically Saturated Models of Arithmetic

Arithmetically saturated models of arithmetic
descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Oct 1995Publisher:Duke University PressJournal:Notre Dame Journal of Formal Logic, volume 36 (issn: 0029-4527, Copyright policy )
Authors: Kossak, Roman; Schmerl, James H.;

doi: 10.1305/ndjfl/1040136914

Arithmetically Saturated Models of Arithmetic

Abstract

A model of a first-order theory is arithmetically saturated if it is saturated with respect to the types that are arithmetic in the complete types realized in the model. The paper presents an outline of the general theory of countable arithmetically saturated models of PA and some of its applications. The results concern the automorphism group of a countable recursively saturated model of PA. New results on fixed point sets, open subgroups, and the cofinality of the automorphisms group are given. It is also shown that the standard system of a countable arithmetically saturated model of PA is determined by the lattice of the elementary substructures of the model.

Keywords

Models of arithmetic and set theory, Models with special properties (saturated, rigid, etc.), arithmetically saturated models of PA, open subgroups, automorphism group, recursive saturation, 03C57, fixed point, Peano arithmetic, lattice of elementary substructures, 03C62, cofinality

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    		 14
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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
14
Average
Top 10%
Average
Green
hybrid