b-MINIMALITY

DOI10.1142/S0219061307000664zbMath1146.03021arXivmath/0610183OpenAlexW3037994112MaRDI QIDQ3521599

Raf Cluckers, François Loeser

Publication date: 26 August 2008

Published in: Journal of Mathematical Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0610183

zbMATH Keywords

\(p\)-adic numbersdimension theoryHenselian valued fieldstame geometryaxiomatic Cohen-Denef cell decompositiondefinable families of points and balls

Mathematics Subject Classification ID

Model-theoretic algebra (03C60) Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Zeta functions and (L)-functions (11S40) Model theory (number-theoretic aspects) (11U09) Model theory of ordered structures; o-minimality (03C64) Model theory of fields (12L12) Quantifier elimination, model completeness, and related topics (03C10) Valued fields (12J10) Formally (p)-adic fields (12J12)

Related Items (22)

A version of p-adic minimality ⋮ Point counting and Wilkie's conjecture for non-Archimedean Pfaffian and Noetherian functions ⋮ Integration of functions of motivic exponential class, uniform in all non-archimedean local fields of characteristic zero ⋮ Definable functions and stratifications in power-bounded \(T\)-convex fields ⋮ Non-Archimedean Whitney stratifications ⋮ A motivic local Cauchy-Crofton formula ⋮ NON-ARCHIMEDEAN YOMDIN–GROMOV PARAMETRIZATIONS AND POINTS OF BOUNDED HEIGHT ⋮ Motivic local density ⋮ A nonarchimedean Ax-Lindemann theorem ⋮ Hensel minimality II: Mixed characteristic and a diophantine application ⋮ A note on tropicalization in the context of Berkovich spaces ⋮ Non‐archimedean stratifications of tangent cones ⋮ Uniform Yomdin-Gromov parametrizations and points of bounded height in valued fields ⋮ Special transformations in algebraically closed valued fields ⋮ Some results of algebraic geometry over Henselian rank one valued fields ⋮ SOME PROPERTIES OF ANALYTIC DIFFERENCE VALUED FIELDS ⋮ TOPOLOGICAL CELL DECOMPOSITION AND DIMENSION THEORY IN P-MINIMAL FIELDS ⋮ Fields with analytic structure ⋮ p-adically closed fields with nonstandard analytic structure ⋮ Relative decidability and definability in henselian valued fields ⋮ Uniform rationality of the Poincaré series of definable, analytic equivalence relations on local fields ⋮ Hensel minimality I

Cites Work

• The rationality of the Poincaré series associated to the p-adic points on a variety
• Relative elimination of quantifiers for Henselian valued fields
• The field of reals with a predicate for the powers of two
• An isomorphism theorem for Henselian algebraic extensions of valued fields
• Cell decompositions of \(C\)-minimal structures
• On variants of \(o\)-minimality
• A version of o-minimality for the p-adics
• Analytic $p$-adic cell decomposition and integrals
• Decision procedures for real and p‐adic fields

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