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Journal articles
Cell decomposition and classification of definable sets in p-optimal fields
Abstract : We prove that for p-optimal fields (a very large subclass of p-minimal fields containing all the known examples) a cell decomposition theorem follows from methods going back to Denef's paper [Invent. Math, 77 (1984)]. We derive from it the existence of definable Skolem functions and strong p-minimality. Then we turn to strongly p-optimal fields satisfying the Extreme Value Property (a property which in particular holds in fields which are elementarily equivalent to a p-adic one). For such fields K, we prove that every definable subset of KxK^d whose fibers are inverse images by the valuation of subsets of the value group, are semi-algebraic. Combining the two we get a preparation theorem for definable functions on p-optimal fields satisfying the Extreme Value Property, from which it follows that infinite sets definable over such fields are isomorphic iff they have the same dimension.
Cited literature [14 references]
https://hal.archives-ouvertes.fr/hal-01083119
Contributor : Luck Darnière <>
Submitted on : Friday, February 5, 2016 - 1:38:19 PM
Last modification on : Monday, March 9, 2020 - 6:15:55 PM
Document(s) archivé(s) le : Saturday, November 12, 2016 - 11:02:01 AM
Contributor : Luck Darnière <>
Submitted on : Friday, February 5, 2016 - 1:38:19 PM
Last modification on : Monday, March 9, 2020 - 6:15:55 PM
Document(s) archivé(s) le : Saturday, November 12, 2016 - 11:02:01 AM
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