Publikation: On the value group of a model of Peano Arithmetic
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2017
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Forum Mathematicum. 2017, 29(4), pp. 951-957. ISSN 0933-7741. eISSN 1435-5337. Available under: doi: 10.1515/forum-2015-0226
Zusammenfassung
We investigate IPA-real closed fields, that is, real closed fields which admit an integer part whose non-negative cone is a model of Peano arithmetic. We show that the value group of an IPA-real closed field is an exponential group in the residue field, and that the converse fails in general. As an application, we classify (up to isomorphism) value groups of countable recursively saturated exponential real closed fields. We exploit this characterization to construct countable exponential real closed fields which are not IPA-real closed fields.
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Fachgebiet (DDC)
510 Mathematik
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Left exponentiation; natural valuation; value group; residue field; valuation rank,power series fields; maximally valued fields; ordered fields; integer parts; recursive saturation
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CARL, Merlin, Paola D’AQUINO, Salma KUHLMANN, 2017. On the value group of a model of Peano Arithmetic. In: Forum Mathematicum. 2017, 29(4), pp. 951-957. ISSN 0933-7741. eISSN 1435-5337. Available under: doi: 10.1515/forum-2015-0226BibTex
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title={On the value group of a model of Peano Arithmetic},
number={4},
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journal={Forum Mathematicum},
pages={951--957},
author={Carl, Merlin and D’Aquino, Paola and Kuhlmann, Salma}
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