## Notre Dame Journal of Formal Logic

### More Automorphism Groups of Countable, Arithmetically Saturated Models of Peano Arithmetic

James H. Schmerl

#### Abstract

There is an infinite set ${\mathcal{T}}$ of Turing-equivalent completions of Peano Arithmetic ($\mathsf{PA}$) such that whenever ${\mathcal{M}}$ and ${\mathcal{N}}$ are nonisomorphic countable, arithmetically saturated models of $\mathsf{PA}$ and $\operatorname{Th}({\mathcal{M}})$, $\operatorname{Th}({\mathcal{N}})\in{\mathcal{T}}$, then $\operatorname{Aut}({\mathcal{M}})\ncong\operatorname{Aut}({\mathcal{N}})$.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 59, Number 4 (2018), 491-496.

Dates
Accepted: 9 May 2016
First available in Project Euclid: 2 October 2018

https://projecteuclid.org/euclid.ndjfl/1538445762

Digital Object Identifier
doi:10.1215/00294527-2018-0009

Mathematical Reviews number (MathSciNet)
MR3871897

Zentralblatt MATH identifier
06996540

#### Citation

Schmerl, James H. More Automorphism Groups of Countable, Arithmetically Saturated Models of Peano Arithmetic. Notre Dame J. Formal Logic 59 (2018), no. 4, 491--496. doi:10.1215/00294527-2018-0009. https://projecteuclid.org/euclid.ndjfl/1538445762

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