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Real closed valued fields with analytic structure

Part of: Non-Archimedean analysis Model theory

Published online by Cambridge University Press:  05 December 2019

Pablo Cubides Kovacsics  and
Deirdre Haskell
Pablo Cubides Kovacsics
Affiliation:
TU Dresden, Fachrichtung Mathematik, Institut für Algebra, 01062Dresden, Germany (pablo.cubides_kovacsics@tu-dresden.de)
Deirdre Haskell
Affiliation:
Department of Mathematics and Statistics, McMaster University, 1280 Main St W, Hamilton, ON L8S 4K1, Canada (haskell@math.mcmaster.ca)
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Abstract

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We show quantifier elimination theorems for real closed valued fields with separated analytic structure and overconvergent analytic structure in their natural one-sorted languages and deduce that such structures are weakly o-minimal. We also provide a short proof that algebraically closed valued fields with separated analytic structure (in any rank) are C-minimal.

Keywords

real closed valued fieldsseparated analytic structureoverconvergent power serieso-minimalityweak o-minimalityC-minimality

MSC classification

Primary: 32P05: Non-Archimedean analysis (should also be assigned at least one other classification number from Section 32 describing the type of problem) 32B05: Analytic algebras and generalizations, preparation theorems 03C10: Quantifier elimination, model completeness and related topics 03C64: Model theory of ordered structures; o-minimality
Secondary: 14P10: Semialgebraic sets and related spaces
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 1 , February 2020 , pp. 249 - 261
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
Copyright © Edinburgh Mathematical Society 2019

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