June 2012 A version of p-adic minimality
Raf Cluckers, Eva Leenknegt
J. Symbolic Logic 77(2): 621-630 (June 2012). DOI: 10.2178/jsl/1333566641


We introduce a very weak language ℒM on p-adic fields K, which is just rich enough to have exactly the same definable subsets of the line K that one has using the ring language. (In our context, definable always means definable with parameters.) We prove that the only definable functions in the language ℒM are trivial functions. We also give a definitional expansion ℒM' of ℒM in which K has quantifier elimination, and we obtain a cell decomposition result for ℒM-definable sets.

Our language ℒM can serve as a p-adic analogue of the very weak language (<) on the real numbers, to define a notion of minimality on the field of p-adic numbers and on related valued fields. These fields are not necessarily Henselian and may have positive characteristic.


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Raf Cluckers. Eva Leenknegt. "A version of p-adic minimality." J. Symbolic Logic 77 (2) 621 - 630, June 2012. https://doi.org/10.2178/jsl/1333566641


Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1251.03042
MathSciNet: MR2963025
Digital Object Identifier: 10.2178/jsl/1333566641

Primary: 03C07 , 03C10
Secondary: 03C64 , 11U09

Keywords: cell decomposition , definability , O-minimality , p-adic numbers , P-minimality , quantifier elimination

Rights: Copyright © 2012 Association for Symbolic Logic


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Vol.77 • No. 2 • June 2012
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