Extending Tamm's theorem

DOI10.5802/aif.1438zbMath0816.32004OpenAlexW2325667551MaRDI QIDQ1891337

Chris Miller, L. P. D. van den Dries

Publication date: 30 May 1995

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1994__44_5_1367_0

zbMATH Keywords

o-minimal structurePuiseux expansionreal analyticGateaux derivativequasianalyticfinitely subanalyticpolynomially bounded structureTarski-Seidenberg property

Mathematics Subject Classification ID

Real-analytic and semi-analytic sets (14P15) (C^infty)-functions, quasi-analytic functions (26E10) Semi-analytic sets, subanalytic sets, and generalizations (32B20) Real-analytic functions (26E05) Models of other mathematical theories (03C65) Quantifier elimination, model completeness, and related topics (03C10) Real-analytic manifolds, real-analytic spaces (32C05)

Related Items

Global complexification of real analytic globally subanalytic functions, An extension of Hölder's theorem on the Gamma function, Complex continuations of ℝ_an,exp-definable unary functions with a diophantine application, Flatness and smooth points of \(p\)-adic subanalytic sets, Geometric categories and o-minimal structures, Integration of semialgebraic functions and integrated Nash functions, Closure and connected component of a planar global semianalytic set defined by analytic functions definable in o-minimal structure, Restricted log-exp-analytic power functions, On preparation theorems for R_{an, exp}-definable functions, LOCAL INTERDEFINABILITY OF WEIERSTRASS ELLIPTIC FUNCTIONS, \(K\)-subanalytic rectilinearization and uniformization, \(R\)-analytic functions, Differentiability properties of log-analytic functions, Restricted log-exp-analytic functions and some differentiability results, Piecewise Weierstrass preparation and division for o-minimal holomorphic functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(p\)-adic and real subanalytic sets
• Point réguliers d'un sous-analytique. (Regular points of a subanalytic set)
• Semianalytic and subanalytic sets
• Subanalytic sets in the calculus of variation
• On the real exponential field with restricted analytic functions
• Expansions of the real field with power functions
• The elementary theory of restricted analytic fields with exponentiation
• Topologically Noetherian analytic algebras. Khovanskij's theory
• A generalization of the Tarski-Seidenberg theorem, and some nondefinability results
• Definable Sets in Ordered Structures. I
• Definable Sets in Ordered Structures. II
• Semi-Algebraic Local-Triviality in Semi-Algebraic Mappings
• Exponentiation is Hard to Avoid
• Infinite Differentiability in Polynomially Bounded O-Minimal Structures
• Analytic functions in topological vector-spaces
• Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function