### 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 language | English (US) |
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Pages (from-to) | 198-204 |

Number of pages | 7 |

Journal | Mathematical Logic Quarterly |

Volume | 56 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2010 |

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### All Science Journal Classification (ASJC) codes

- Logic

### Cite this

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*Mathematical Logic Quarterly*, vol. 56, no. 2, pp. 198-204. https://doi.org/10.1002/malq.200810045

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

Research output: Contribution to journal › Article

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 -