Models of true arithmetic are integer parts of models of real exponentation

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2021
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Journal of Logic and Analysis. Department of Philosophy, Carnegie Mellon University. 2021, (13), 3. ISSN 1759-9008. Available under: doi: 10.4115/jla.2021.13.3
Zusammenfassung

Exploring further the connection between exponentiation on real closed fields and the existence of an integer part modelling strong fragments of arithmetic, we demonstrate that each model of true arithmetic is an integer part of an exponential real closed field that is elementarily equivalent to the real numbers with exponentiation and that each model of Peano arithmetic is an integer part of a real closed field that admits an isomorphism between its ordered additive and its ordered multiplicative group of positive elements. Under the assumption of Schanuel’s Conjecture, we obtain further strengthenings for the last statement.

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Fachgebiet (DDC)
510 Mathematik
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true arithmetic, Peano arithmetic; integer parts; real exponentiation; exponential fields
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ISO 690CARL, Merlin, Lothar Sebastian KRAPP, 2021. Models of true arithmetic are integer parts of models of real exponentation. In: Journal of Logic and Analysis. Department of Philosophy, Carnegie Mellon University. 2021, (13), 3. ISSN 1759-9008. Available under: doi: 10.4115/jla.2021.13.3
BibTex
@article{Carl2021Model-54344,
  year={2021},
  doi={10.4115/jla.2021.13.3},
  title={Models of true arithmetic are integer parts of models of real exponentation},
  number={13},
  volume={},
  issn={1759-9008},
  journal={Journal of Logic and Analysis},
  author={Carl, Merlin and Krapp, Lothar Sebastian},
  note={Article Number: 3}
}
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