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An existential ∅-definition of Fq[[t]]Fq[[t]] IN Fq(t)

Abstract:

We show that the valuation ring Fq [[t]] in the local field Fq ((t)) is existentially definable in the language of rings with no parameters. The method is to use the definition of the henselian topology following the work of Prestel-Ziegler to give an ∃-Fq -definable bounded neighbouhood of 0. Then we “tweak” this set by subtracting, taking roots, and applying Hensel’s Lemma in order to find an ∃-Fq -definable subset of Fq [[t]] which contains tFq [[t]]. Finall...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1017/jsl.2014.27

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Cambridge University Press
Journal:
Journal of Symbolic Logic More from this journal
Volume:
79
Issue:
4
Pages:
1336-1343
Publication date:
2014-12-31
DOI:
EISSN:
1943-5886
ISSN:
0022-4812
Keywords:
Pubs id:
pubs:414384
UUID:
uuid:fc1a93b2-cf61-463d-80a2-9bec32a29d3d
Local pid:
pubs:414384
Source identifiers:
414384
Deposit date:
2017-09-15

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