publication . Article . Preprint . 2018

Imaginaries in separably closed valued fields

Martin Hils; Moshe Kamensky; Silvain Rideau;
Open Access English
  • Published: 01 Jun 2018
  • Publisher: HAL CCSD
  • Country: France
Abstract
We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets to study stably dominated types in those structures. We show that separably closed valued fields of finite imperfection degree are metastable and that the space of stably dominated types is strict pro-definable.
Persistent Identifiers
Subjects
free text keywords: [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], Mathematics - Logic, 12J20, 03C10, 03C98, General Mathematics, Algebra, Mathematics
Funded by
EC| MODAG
Project
MODAG
Model Theory and asymptotic geometry
  • Funder: European Commission (EC)
  • Project Code: 291111
  • Funding stream: FP7 | SP2 | ERC
,
ANR| ValCoMo
Project
ValCoMo
Valuations, Combinatorics and Model Theory
  • Funder: French National Research Agency (ANR) (ANR)
  • Project Code: ANR-13-BS01-0006
30 references, page 1 of 2

[1] Zo´e Chatzidakis and Ehud Hrushovski. Model theory of difference fields. Trans. Amer. Math. Soc., 351(8):2997-3071, 1999. [OpenAIRE]

[2] Artem Chernikov and Itay Kaplan. Forking and dividing in NTP2 theories. J. Symbolic Logic, 77(1):1-20, 2012.

[3] Franc¸oise Delon. Id´eaux et types sur les corps s´eparablement clos. M´em. Soc. Math. France (N.S.), 33:76, 1988.

[4] Franc¸oise Delon. Separably closed fields. In Model theory and algebraic geometry, volume 1696 of Lecture Notes in Math., pages 143-176. Springer, Berlin, 1998.

[5] Franc¸oise Delon. Quantifier elimination in pairs of algebraically closed fields. Confluentes Math., 4(2), 2012.

[6] Antoine Ducros. Les espaces de Berkovich sont mod´er´es (d'apr`es Ehud Hrushovski et Fran¸cois Loeser). Ast´erisque, 352:Exp. No. 1056, x, 459-507, 2013. S´eminaire Bourbaki. Vol. 2011/2012. Expos´es 1043-1058.

[7] Ju. L. Ershov. Fields with a solvable theory. Dokl. Akad. Nauk SSSR, 174:19-20, 1967.

[8] Deirdre Haskell, Ehud Hrushovski, and Dugald Macpherson. Definable sets in algebraically closed valued fields: elimination of imaginaries. J. Reine Angew. Math., 597:175-236, 2006.

[9] Deirdre Haskell, Ehud Hrushovski, and Dugald Macpherson. Stable domination and independence in algebraically closed valued fields, volume 30 of Lecture Notes in Logic. Association for Symbolic Logic, Chicago, IL, 2008.

[10] Daniel Hoffmann. Witt vectors and separably closed fields with higher derivations. arXiv:1510.00218.

[11] Jizhan Hong. Immediate expansions by valuation of fields. PhD thesis, McMaster University, 2013. [OpenAIRE]

[12] Jizhan Hong. Separably closed valued fields: quantifier elimination. J. Symbolic Logic, 81(3):887-900, 2016.

[13] Ehud Hrushovski. The Mordell-Lang conjecture for function fields. J. Amer. Math. Soc., 9(3):667-690, 1996.

[14] Ehud Hrushovski and Franc¸ois Loeser. Non-archimedean tame topology and stably dominated types, volume 192 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 2016. [OpenAIRE]

[15] Ehud Hrushovski, Ben Martin, and Silvain Rideau. Zeta functions from definable equivalence relations. arXiv:math/0701011v4, with an appendix by Raf Cluckers.

30 references, page 1 of 2
Any information missing or wrong?Report an Issue