Interstitial and pseudo gaps in models of Peano Arithmetic

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic a is a maximal subgroup of Aut(M) if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ⊂ M is a very good interstice, and a ∈ Ω, then the stabilizer of a is a maximal subgroup of Aut(M) if and only if the type of a is selective and rational.

Original languageEnglish (US)
Pages (from-to)198-204
Number of pages7
JournalMathematical Logic Quarterly
Volume56
Issue number2
DOIs
StatePublished - Mar 1 2010

Fingerprint

Pseudogap
Peano Arithmetic
Maximal Subgroup
Countable
If and only if
Automorphism Group
Model

All Science Journal Classification (ASJC) codes

  • Logic

Cite this

@article{11f5848ecdae4a3e9de8ce87cc463341,
title = "Interstitial and pseudo gaps in models of Peano Arithmetic",
abstract = "In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic a is a maximal subgroup of Aut(M) if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ⊂ M is a very good interstice, and a ∈ Ω, then the stabilizer of a is a maximal subgroup of Aut(M) if and only if the type of a is selective and rational.",
author = "Nurkhaidarov, {Ermek S.}",
year = "2010",
month = "3",
day = "1",
doi = "10.1002/malq.200810045",
language = "English (US)",
volume = "56",
pages = "198--204",
journal = "Mathematical Logic Quarterly",
issn = "0942-5616",
publisher = "Wiley-VCH Verlag",
number = "2",

}

Interstitial and pseudo gaps in models of Peano Arithmetic. / Nurkhaidarov, Ermek S.

In: Mathematical Logic Quarterly, Vol. 56, No. 2, 01.03.2010, p. 198-204.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Interstitial and pseudo gaps in models of Peano Arithmetic

AU - Nurkhaidarov, Ermek S.

PY - 2010/3/1

Y1 - 2010/3/1

N2 - In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic a is a maximal subgroup of Aut(M) if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ⊂ M is a very good interstice, and a ∈ Ω, then the stabilizer of a is a maximal subgroup of Aut(M) if and only if the type of a is selective and rational.

AB - In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic a is a maximal subgroup of Aut(M) if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ⊂ M is a very good interstice, and a ∈ Ω, then the stabilizer of a is a maximal subgroup of Aut(M) if and only if the type of a is selective and rational.

UR - http://www.scopus.com/inward/record.url?scp=77953346439&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77953346439&partnerID=8YFLogxK

U2 - 10.1002/malq.200810045

DO - 10.1002/malq.200810045

M3 - Article

AN - SCOPUS:77953346439

VL - 56

SP - 198

EP - 204

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

SN - 0942-5616

IS - 2

ER -