Nonstandard models that are definable in models of Peano Arithmetic
The work
| Authors | Kazuma Ikeda; Akito Tsuboi |
|---|---|
| Type | article |
| Year | 2007 |
| Citekey | ikeda2007nonstandard |
Where it appeared
| Published in | Mathematical logic quarterly |
|---|---|
| Publisher | Wiley |
| Volume | 53 |
| Issue | 1 |
| Pages | 27--37 |
Identifiers
| DOI | 10.1002/malq.200610020 |
|---|
Access
| Landing page | https://doi.org/10.1002/malq.200610020 |
|---|
Abstract
In this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model *N* without parameters in a model *M*, we show that *N* is isomorphic to *M* if *M* is elementary extension of the standard model and *N* is elementarily equivalent to *M*. On the other hand, we show that there is a model *M* and a definable model *N* with parameters in *M* such that *N* is elementarily equivalent to *M* but *N* is not isomorphic to *M*. We also show that there is a model *M* and a definable model *N* with parameters in *M* such that *N* is elementarily equivalent to *M*, and *N* is isomorphic to *M*, but *N* is not definably isomorphic to *M*. And also, we give a generalization of Tennenbaum's theorem. At the end, we give a new method to construct a definable model by a refinement of Kotlarski's method.
How it got here
| How it got here | agent via unpaywall |
|---|---|
| Added | 2026-08-08 00:00 UTC |
| Not denied by | a person 2026-08-16 17:20 UTC |
Filed under
Cite it as
@article{ikeda2007nonstandard,
title = {Nonstandard models that are definable in models of Peano Arithmetic},
author = {Kazuma Ikeda and Akito Tsuboi},
year = {2007},
journal = {Mathematical logic quarterly},
volume = {53},
number = {1},
pages = {27--37},
publisher = {Wiley},
doi = {10.1002/malq.200610020},
}
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