Journal article

Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields

Abstract:: We define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multiplicative group of a local field of characteristic zero are finite-by-Presburger and interpret the higher residue rings of the local field. We apply these results to give a new proof of the model completeness in the ring language of a local field of characteristic zero (a result that follows also from work of Prestel-Roquette).

Publication status:: Not published

Peer review status:: Not peer reviewed

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APA Style

Derakhshan, J., & Macintyre, A. (2016). Model theory of finite-by-Presburger Abelian groups and finite extensions of $p$-adic fields. ArXiv.

MLA Style

Derakhshan, J., and A. Macintyre. “Model Theory of Finite-by-Presburger Abelian Groups and Finite Extensions of $p$-Adic Fields.” ArXiv, Cornell University, 2016.

Chicago Style

Derakhshan, J, and A Macintyre. 2016. “Model Theory of Finite-by-Presburger Abelian Groups and Finite Extensions of $p$-Adic Fields.” ArXiv.
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Files:: 1603.08601v1.pdf

(Preview, Author's original, pdf, 166.3KB, Terms of use)

Authors

+ Derakhshan, J More by this author

Institution:: University of Oxford
Division:: MPLS
Department:: Computer Science
Oxford college:: Merton College
Role:: Author

+ Macintyre, A More by this author

Role:: Author

Publisher:: Cornell University
Journal:: arXiv More from this journal
Publication date:: 2016-03-29

Keywords:: 03C10, 03C60, 03C65, 12E30, 12J20, 12J25, 12J12, 11U09

FFR

math.LO
Pubs id:: pubs:614617
UUID:: uuid:00ff3f5d-210d-440b-a7bd-4a1d4a54f228
Local pid:: pubs:614617
Source identifiers:: 614617
Deposit date:: 2017-10-20

Terms of use

Copyright date:: 2016
Notes:: © The Authors. This is an arXiv preprint and is available at: https://arxiv.org/abs/1603.08601

Licence:: Terms and Conditions of Use for Oxford University Research Archive

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