Alex Wilkie | Academic Influence

Alex Wilkie's AcademicInfluence.com Rankings

Alex Wilkie

Mathematics

#769

World Rank

#1390

Historical Rank

Measure Theory

#2443

World Rank

#2926

Historical Rank

mathematics Degrees

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Mathematics

Alex Wilkie's Degrees

PhD Mathematics Princeton University
Masters Mathematics University of Oxford

Why Is Alex Wilkie Influential?

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According to Wikipedia, Alex James Wilkie FRS is a British mathematician known for his contributions to model theory and logic. Previously Reader in Mathematical Logic at the University of Oxford, he was appointed to the Fielden Chair of Pure Mathematics at the University of Manchester in 2007.

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Alex Wilkie's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function (1996) (471)
TAME TOPOLOGY AND O-MINIMAL STRUCTURES (London Mathematical Society Lecture Note Series 248) By L OU VAN DEN D RIES : 180 pp., £24.95 (US$39.95, LMS Members' price £18.70), ISBN 0 521 59838 9 (Cambridge University Press, 1998). (2000) (422)
Model theory with applications to algebra and analysis (2008) (319)
On the scheme of induction for bounded arithmetic formulas (1987) (232)
The rational points of a definable set (2006) (223)
Gromov's theorem on groups of polynomial growth and elementary logic (1984) (219)
Quasianalytic Denjoy-Carleman classes and o-minimality (2003) (189)
THE CLASSICAL DECISION PROBLEM (Perspectives in Mathematical Logic) By Egon Börger, Erich Grädel and Yuri Gurevich: 482 pp., DM.158.–, ISBN 3 540 57073 X (Springer, 1997). (1998) (186)
On the decidability of the real exponential field (1996) (185)
Counting problems in bounded arithmetic (1985) (165)
Provability of the pigeonhole principle and the existence of infinitely many primes (1988) (147)
A theorem of the complement and some new o-minimal structures (1999) (127)
Model theory of algebra and arithmetic (1980) (93)
Some Results and Problems on Weak Systems of Arithmetic (1978) (65)
Speculative Research : The Lure of Possible Futures (2017) (60)
Counting $Δ_0$ sets (1987) (49)
Inventing the social (2018) (45)
On the Existence of end Extensions of Models of Bounded Induction (1989) (39)
An effective bound for groups of linear growth (1984) (33)
O-MINIMAL STRUCTURES (2007) (26)
A survey of asymptotic classes and measurable structures (2008) (25)
A Schanuel property for exponentially transcendental powers (2008) (23)
Schanuel’s Conjecture and the Decidability of the Real Exponential Field (1997) (21)
On Exponentiation - A Solution to Tarski's High School Algebra Problem (2001) (21)
The Lure of Possible Futures: On Speculative Research (2017) (21)
O-Minimality and Diophantine Geometry (2015) (19)
Uniform parameterization of subanalytic sets and diophantine applications (2016) (19)
On Sentences Interpretrble in Systems of Arithmetic (1986) (18)
Locally polynomially bounded structures (2007) (18)
Creative Assemblages: Organisation and Outputs of Practice-Led Research (2010) (18)
Schanuel's conjecture for non-isoconstant elliptic curves over function fields (2008) (17)
Ax-Schanuel and o-minimality (2015) (17)
Applications of complexity theory to Σo-definability Problems in arithmetic (1980) (16)
On the theories of end-extensions of models of arithmetic (1977) (15)
Some observations about the real and imaginary parts of complex Pfaffian functions (2008) (15)
Diophantine properties of sets definable in o-minimal structures (2004) (12)
On defining C∞ (1994) (11)
Some local definability theory for holomorphic functions (2008) (11)
On models of arithmetic—Answers to two problems raised by H. Gaifman (1975) (11)
On the theory of the real exponential field (1989) (11)
Model Theory in Algebra, Analysis and Arithmetic (2014) (10)
Introduction: From performance to inventing the social (2018) (9)
On models of arithmetic having non-modular substructure lattices (1977) (8)
Rational points on definable sets (2015) (7)
Expeditionary Learning Outward Bound. Summary Report. (1996) (6)
The laws of integer divisibility, and solution sets of linear divisibility conditions (2003) (6)
Introduction to abelian varieties and the Ax–Lindemann–Weierstrass theorem (2015) (6)
The real field with an irrational power function and a dense multiplicative subgroup (2008) (5)
Models and Computability: Model Theory of Analytic and Smooth Functions (1999) (5)
Some Results and Problems on Complex Germs with Definable Mittag-Leffler Stars (2013) (4)
Models of number theory (1972) (4)
Complex continuations of ℝan,exp‐definable unary functions with a diophantine application (2016) (4)
Lectures on elimination theory for semialgebraic and subanalytic sets (2015) (3)
Integer‐valued definable functions (2012) (3)
On discretely ordered rings in which every definable ideal is principal (1981) (2)
2008 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '08 (2009) (2)
Fusing o-minimal structures (2005) (2)
On Core Structures for Peano Arithmetic (1982) (1)
Classification of Quantifier Prefixes Over Exponential Diophantine Equations (1986) (1)
Review: Edward Nelson, Predicative arithmetic (1990) (1)
Section Introduction: Speculative techniques (2017) (1)
Review: Samuel R. Buss, Bounded Arithmetic (1991) (1)
'Speculation and Speculative Research Workshop', International Workshop with participants from UK, US, and Australia on speculation in social and cultural research and STS (2014) (1)
Studios, Problems, Publics (2018) (1)
Model Theory with Applications to Algebra and Analysis: Volume 1 (2008) (1)
Controversy and Publics: Mapping Issue Networks (2009) (0)
Model Theory of Algebra and Arithmetic Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic Held at Karpacz, Poland, September 1-7, 1979 (1980) (0)
Inventive tensions: A conversation (2018) (0)
Reconstruction Theorems for Families of Sets (1978) (0)
O-Minimality and its Applications to Number Theory and Analysis (2018) (0)
Lectures on the Model Theory of Real and Complex Exponentiation (2014) (0)
Section 2: Speculative lures (2017) (0)
Czechoslovak Academy of Sciences Prague (0)
ASSOCIATION FOR SYMBOLIC LOGIC (2018) (0)
Preface - Logic Colloquium '94, 21-30 July 1994, Clermont-Ferrand, France (1997) (0)
A Note on Products of Finite Structures with an Application to Graphs (1976) (0)
Creating Better Visualisations With STS (2020) (0)
Theorem 5.1 Revisited (2007) (0)
Participation, Translation & Accountability (2010) (0)
Note on Quantifier Prefixes Over Diophantine Equations.Classification of Quantifier Prefixes over Exponential Diophantine Equations (1988) (0)
Learning Design Through Social Science (2014) (0)
Model Theory with Applications to Algebra and Analysis: Preface (2008) (0)
1 Locally tame functions (0)
Enacting Users, Mediating Publics (2010) (0)
A combinatorial method of tackling the problem of hierarchy collapse , and a theorem of Ajtai (2010) (0)
La Sorbonne, Paris, France, July 23–31, 2000 (2001) (0)
2000 European Summer Meeting of the Association for Symbolic Logic Logic Colloquium 2000 (2001) (0)
Logic Colloquium '84 Proceedings of the Colloquium Held in Manchester, U.K., July 1984 (1986) (0)
O-minimality and diophantine applications (2019) (0)
Review: J. B. Paris, L. Pacholski, J. Wierzejewski, A. J. Wilkie, A Hierarchy of Cuts in Models of Arithmetic; George Mills, A Tree Analysis of Unprovable Combinatorial Statements; Jussi Ketonen, Robert Solovay, Rapidly Growing Ramsey Functions (1986) (0)
Section Introduction: Speculative implications (2017) (0)
European summer meeting of the Association for Symbolic Logic, Manchester, England, 1984 (1986) (0)
Mapping Issues, Topics and Controversies (2009) (0)
1997 european summer meeting of the association for symbolic logic (1998) (0)
On Defining Cinfty (1994) (0)
Model theory in algebra, analysis and arithmetic : Cetraro, Italy 2012 (2014) (0)
Attaching Ethnographic Users to Objects (2009) (0)
Section Introduction: Speculative Propositions (2017) (0)
The rational points of a definable set Pila (2017) (0)

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