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Wilkie, Alex James

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Author ID: wilkie.alex-j Recent zbMATH articles by "Wilkie, Alex James"
Published as: Wilkie, A.; Wilkie, A. J.; Wilkie, Alex; Wilkie, Alex J.
Homepage: https://www.maths.ox.ac.uk/people/alex.wilkie
External Links: MGP · Wikidata · dblp
Documents Indexed: 59 Publications since 1975, including 8 Books
Biographic References: 1 Publication

Publications by Year

Citations contained in zbMATH

44 Publications have been cited 685 times in 532 Documents Cited by Year
Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function. Zbl 0892.03013
Wilkie, A. J.
139
1996
On the scheme of induction for bounded arithmetic formulas. Zbl 0647.03046
Wilkie, A. J.; Paris, J. B.
78
1987
Gromov’s theorem on groups of polynomial growth and elementary logic. Zbl 0552.20017
van den Dries, Lou; Wilkie, A. J.
70
1984
The rational points of a definable set. Zbl 1217.11066
Pila, J.; Wilkie, A. J.
64
2006
Quasianalytic Denjoy-Carleman classes and o-minimality. Zbl 1095.26018
Rolin, J.-P.; Speissegger, P.; Wilkie, A. J.
59
2003
Provability of the pigeonhole principle and the existence of infinitely many primes. Zbl 0688.03042
Paris, J. B.; Wilkie, A. J.; Woods, A. R.
55
1988
A theorem of the complement and some new o-minimal structures. Zbl 0948.03037
Wilkie, A. J.
38
1999
On the decidability of the real exponential field. Zbl 0896.03012
Macintyre, Angus; Wilkie, A. J.
33
1996
Counting problems in bounded arithmetic. Zbl 0572.03034
Paris, J.; Wilkie, A.
28
1985
Some results and problems on weak systems of arithmetic. Zbl 0449.03076
Wilkie, A. J.
16
1978
An effective bound for groups of linear growth. Zbl 0567.20016
Wilkie, A. J.; van den Dries, Lou
15
1984
On the existence of end extensions of models of bounded induction. Zbl 0695.03019
Wilkie, A.; Paris, J.
8
1989
Counting \(\Delta _ 0\) sets. Zbl 0627.03018
Paris, J.; Wilkie, A.
7
1987
Locally polynomially bounded structures. Zbl 1146.03023
Jones, G. O.; Wilkie, A. J.
6
2008
On defining \(C^ \infty\). Zbl 0808.03023
Wilkie, A. J.
5
1994
On models of arithmetic - answers to two problems raised by H. Gaifman. Zbl 0319.02050
Wilkie, Alex
5
1975
On the theory of the real exponential field. Zbl 0659.03013
Wilkie, A. J.
4
1989
On sentences interpretable in systems of arithmetic. Zbl 0603.03018
Wilkie, A. J.
4
1986
Models of arithmetic and the rudimentary sets. Zbl 0499.03021
Wilkie, A. J.; Paris, J. B.
4
1981
Applications of complexity theory to \(Sigma_ 0-\)definability problems in arithmetic. Zbl 0483.03024
Wilkie, A. J.
4
1980
o-minimal structures. Zbl 1197.03043
Wilkie, Alex J.
3
2009
Diophantine properties of sets definable in o-minimal structures. Zbl 1081.03038
Wilkie, A. J.
3
2004
On exponentiation – a solution to Tarski’s high school algebra problem. Zbl 0993.03044
Wilkie, Alex J.
3
2000
Model theory of analytic and smooth functions. Zbl 0943.03030
Wilkie, Alex J.
3
1999
Characterizing some low arithmetic classes. Zbl 0635.03033
Paris, J. B.; Handley, W. G.; Wilkie, A. J.
3
1986
On the theories of end-extensions of models of arithmetic. Zbl 0376.02043
Wilkie, A. J.
3
1977
Complex continuations of \(\mathbb{R}_{\mathrm{an},\exp}\)-definable unary functions with a Diophantine application. Zbl 06618262
Wilkie, A. J.
2
2016
A Schanuel property for exponentially transcendental powers. Zbl 1223.11093
Bays, Martin; Kirby, Jonathan; Wilkie, A. J.
2
2010
Some local definability theory for holomorphic functions. Zbl 1152.03020
Wilkie, A. J.
2
2008
Liouville functions. Zbl 1098.03044
Wilkie, A. J.
2
2005
The laws of integer divisibility, and solution sets of linear divisibility conditions. Zbl 1056.03020
van den Dries, L.; Wilkie, A. J.
2
2003
Schanuel’s conjecture and the decidability of the real exponential field. Zbl 0888.03022
Wilkie, A. J.
2
1997
On models of arithmetic having non-modular substructure lattices. Zbl 0365.02041
Wilkie, A. J.
2
1977
Uniform parameterization of subanalytic sets and Diophantine applications. Zbl 07201735
Cluckers, Raf; Pila, Jonathan; Wilkie, Alex
1
2020
Lectures on elimination theory for semialgebraic and subanalytic sets. Zbl 1388.03039
Wilkie, A. J.
1
2015
Rational points on definable sets. Zbl 1416.11120
Wilkie, A. J.
1
2015
Integer-valued definable functions. Zbl 1275.03130
Jones, G. O.; Thomas, M. E. M.; Wilkie, A. J.
1
2012
Model theory with applications to algebra and analysis. Vol. 1. Zbl 1144.03004
Chatzidakis, Zoé (ed.); Macpherson, Dugald (ed.); Pillay, Anand (ed.); Wilkie, Alex (ed.)
1
2008
Model theory and applications. Based on the Euro-Conference in model theory and applications, Ravello, Italy, May 27–June 1, 2002. Zbl 1066.03014
Bélair, L. (ed.); Chatzidakis, Z. (ed.); D’Aquino, P. D. (ed.); Marker, D. (ed.); Otero, M. (ed.); Point, F. (ed.); Wilkie, A. (ed.)
1
2002
o-minimality. Zbl 0906.03038
Wilkie, A. J.
1
1998
Modèles nonstandard en arithmétiques et théorie des ensembles. Zbl 0631.03048
Ressayre, J. P.; Wilkie, A. J.
1
1986
On core structures for Peano arithmetic. Zbl 0517.03030
Wilkie, A. J.
1
1982
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. Zbl 0436.00008
Pacholski, L. (ed.); Wierzejewski, J. (ed.); Wilkie, A. J. (ed.)
1
1980
A note on products of finite structures with an application to graphs. Zbl 0352.08011
Wilkie, A. J.
1
1976
Uniform parameterization of subanalytic sets and Diophantine applications. Zbl 07201735
Cluckers, Raf; Pila, Jonathan; Wilkie, Alex
1
2020
Complex continuations of \(\mathbb{R}_{\mathrm{an},\exp}\)-definable unary functions with a Diophantine application. Zbl 06618262
Wilkie, A. J.
2
2016
Lectures on elimination theory for semialgebraic and subanalytic sets. Zbl 1388.03039
Wilkie, A. J.
1
2015
Rational points on definable sets. Zbl 1416.11120
Wilkie, A. J.
1
2015
Integer-valued definable functions. Zbl 1275.03130
Jones, G. O.; Thomas, M. E. M.; Wilkie, A. J.
1
2012
A Schanuel property for exponentially transcendental powers. Zbl 1223.11093
Bays, Martin; Kirby, Jonathan; Wilkie, A. J.
2
2010
o-minimal structures. Zbl 1197.03043
Wilkie, Alex J.
3
2009
Locally polynomially bounded structures. Zbl 1146.03023
Jones, G. O.; Wilkie, A. J.
6
2008
Some local definability theory for holomorphic functions. Zbl 1152.03020
Wilkie, A. J.
2
2008
Model theory with applications to algebra and analysis. Vol. 1. Zbl 1144.03004
Chatzidakis, Zoé (ed.); Macpherson, Dugald (ed.); Pillay, Anand (ed.); Wilkie, Alex (ed.)
1
2008
The rational points of a definable set. Zbl 1217.11066
Pila, J.; Wilkie, A. J.
64
2006
Liouville functions. Zbl 1098.03044
Wilkie, A. J.
2
2005
Diophantine properties of sets definable in o-minimal structures. Zbl 1081.03038
Wilkie, A. J.
3
2004
Quasianalytic Denjoy-Carleman classes and o-minimality. Zbl 1095.26018
Rolin, J.-P.; Speissegger, P.; Wilkie, A. J.
59
2003
The laws of integer divisibility, and solution sets of linear divisibility conditions. Zbl 1056.03020
van den Dries, L.; Wilkie, A. J.
2
2003
Model theory and applications. Based on the Euro-Conference in model theory and applications, Ravello, Italy, May 27–June 1, 2002. Zbl 1066.03014
Bélair, L. (ed.); Chatzidakis, Z. (ed.); D’Aquino, P. D. (ed.); Marker, D. (ed.); Otero, M. (ed.); Point, F. (ed.); Wilkie, A. (ed.)
1
2002
On exponentiation – a solution to Tarski’s high school algebra problem. Zbl 0993.03044
Wilkie, Alex J.
3
2000
A theorem of the complement and some new o-minimal structures. Zbl 0948.03037
Wilkie, A. J.
38
1999
Model theory of analytic and smooth functions. Zbl 0943.03030
Wilkie, Alex J.
3
1999
o-minimality. Zbl 0906.03038
Wilkie, A. J.
1
1998
Schanuel’s conjecture and the decidability of the real exponential field. Zbl 0888.03022
Wilkie, A. J.
2
1997
Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function. Zbl 0892.03013
Wilkie, A. J.
139
1996
On the decidability of the real exponential field. Zbl 0896.03012
Macintyre, Angus; Wilkie, A. J.
33
1996
On defining \(C^ \infty\). Zbl 0808.03023
Wilkie, A. J.
5
1994
On the existence of end extensions of models of bounded induction. Zbl 0695.03019
Wilkie, A.; Paris, J.
8
1989
On the theory of the real exponential field. Zbl 0659.03013
Wilkie, A. J.
4
1989
Provability of the pigeonhole principle and the existence of infinitely many primes. Zbl 0688.03042
Paris, J. B.; Wilkie, A. J.; Woods, A. R.
55
1988
On the scheme of induction for bounded arithmetic formulas. Zbl 0647.03046
Wilkie, A. J.; Paris, J. B.
78
1987
Counting \(\Delta _ 0\) sets. Zbl 0627.03018
Paris, J.; Wilkie, A.
7
1987
On sentences interpretable in systems of arithmetic. Zbl 0603.03018
Wilkie, A. J.
4
1986
Characterizing some low arithmetic classes. Zbl 0635.03033
Paris, J. B.; Handley, W. G.; Wilkie, A. J.
3
1986
Modèles nonstandard en arithmétiques et théorie des ensembles. Zbl 0631.03048
Ressayre, J. P.; Wilkie, A. J.
1
1986
Counting problems in bounded arithmetic. Zbl 0572.03034
Paris, J.; Wilkie, A.
28
1985
Gromov’s theorem on groups of polynomial growth and elementary logic. Zbl 0552.20017
van den Dries, Lou; Wilkie, A. J.
70
1984
An effective bound for groups of linear growth. Zbl 0567.20016
Wilkie, A. J.; van den Dries, Lou
15
1984
On core structures for Peano arithmetic. Zbl 0517.03030
Wilkie, A. J.
1
1982
Models of arithmetic and the rudimentary sets. Zbl 0499.03021
Wilkie, A. J.; Paris, J. B.
4
1981
Applications of complexity theory to \(Sigma_ 0-\)definability problems in arithmetic. Zbl 0483.03024
Wilkie, A. J.
4
1980
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. Zbl 0436.00008
Pacholski, L. (ed.); Wierzejewski, J. (ed.); Wilkie, A. J. (ed.)
1
1980
Some results and problems on weak systems of arithmetic. Zbl 0449.03076
Wilkie, A. J.
16
1978
On the theories of end-extensions of models of arithmetic. Zbl 0376.02043
Wilkie, A. J.
3
1977
On models of arithmetic having non-modular substructure lattices. Zbl 0365.02041
Wilkie, A. J.
2
1977
A note on products of finite structures with an application to graphs. Zbl 0352.08011
Wilkie, A. J.
1
1976
On models of arithmetic - answers to two problems raised by H. Gaifman. Zbl 0319.02050
Wilkie, Alex
5
1975
all top 5

Cited by 488 Authors

17 Krajíček, Jan
14 D’Aquino, Paola
13 Pila, Jonathan
12 Macintyre, Angus John
12 Visser, Albert
11 Fischer, Andreas M.
9 Buss, Samuel R.
8 van den Dries, Lou
8 Willard, Dan E.
7 Miller, Chris
7 Sapir, Mark Valentinovich
7 Tsimerman, Jacob
6 Berarducci, Alessandro
6 Binyamini, Gal
6 Bowditch, Brian H.
6 Jeřábek, Emil
6 Kołodziejczyk, Leszek Aleksander
6 Kuhlmann, Salma
6 Le Gal, Olivier
6 Servi, Tamara
6 Wilkie, Alex James
5 Bianconi, Ricardo
5 Dimitracopoulos, Costas
5 Druţu, Cornelia
5 Edmundo, Mário J.
5 Kaiser, Tobias
5 Pudlák, Pavel
5 Ressayre, Jean-Pierre
5 Starchenko, Sergei
5 Takeuti, Gaisi
5 Thapen, Neil
5 Yomdin, Yosef
4 Aschenbrenner, Matthias
4 Behrstock, Jason A.
4 Beklemishev, Lev D.
4 Brihaye, Thomas
4 Clote, Peter G.
4 Cornaros, Charalampos
4 Habegger, Philipp
4 Jones, Gareth Owen
4 Marker, David E.
4 Novikov, Dmitry
4 Nowak, Krzysztof Jan
4 Otero, Margarita
4 Pitassi, Toniann
4 Rolin, Jean-Philippe
4 Shelah, Saharon
4 Speissegger, Patrick
4 Terzo, Giuseppina
4 Trofimov, Vladimir Ivanovich
4 Ullmo, Emmanuel
4 van der Hoeven, Joris
4 Yafaev, Andrei
3 Aleksandrova, S. A.
3 Atserias, Albert
3 Bakker, Benjamin
3 Beckmann, Arnold
3 Bierstone, Edward
3 Burguet, David
3 Buss, Sam
3 Cluckers, Raf
3 Cordón-Franco, Andrés
3 Groves, Daniel P.
3 Kirby, Jonathan
3 Kleiner, Bruce
3 Knight, Julia F.
3 Kramer, Linus
3 Lara-Martín, Francisco Felix
3 Lion, Jean-Marie
3 Michaux, Christian
3 Onshuus, Alf Angel
3 Peterzil, Ya’acov
3 Point, Françoise
3 Richardson, Daniel C.
3 Seifter, Norbert
3 Thomas, Margaret E. M.
3 Tressl, Marcus
2 Adamowicz, Zofia
2 Akian, Marianne
2 Baro, Elías
2 Bays, Martin
2 Beame, Paul W.
2 Belotto da Silva, André Ricardo
2 Benedikt, Michael A.
2 Bonet, Maria Luisa
2 Boughattas, Sedki
2 Butler, Lee A.
2 Comte, Georges
2 Cucker, Felipe
2 Daw, Christopher
2 Delon, Françoise
2 Demangos, Luca
2 Dydak, Jerzy
2 Fernández Margarit, Alejandro
2 Fornasiero, Antongiulio
2 Freitag, James
2 Friedman, Harvey M.
2 Gao, Ziyang
2 Gaubert, Stéphane
2 Goldbring, Isaac
...and 388 more Authors
all top 5

Cited in 139 Serials

73 Annals of Pure and Applied Logic
42 The Journal of Symbolic Logic
25 Archive for Mathematical Logic
18 Theoretical Computer Science
14 Annales de l’Institut Fourier
13 Proceedings of the American Mathematical Society
13 Transactions of the American Mathematical Society
12 The Bulletin of Symbolic Logic
11 Notre Dame Journal of Formal Logic
10 Journal of Symbolic Computation
10 Annals of Mathematics. Second Series
9 Mathematical Logic Quarterly (MLQ)
7 Advances in Mathematics
7 Duke Mathematical Journal
7 Information and Computation
7 Comptes Rendus. Mathématique. Académie des Sciences, Paris
6 Israel Journal of Mathematics
6 Journal of Computer and System Sciences
6 International Journal of Algebra and Computation
6 Geometric and Functional Analysis. GAFA
6 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
6 Journal of the Institute of Mathematics of Jussieu
5 Compositio Mathematica
5 Journal of Algebra
5 Journal of Pure and Applied Algebra
5 Journal of the American Mathematical Society
4 Geometriae Dedicata
4 Inventiones Mathematicae
4 Mathematische Annalen
4 Studia Logica
4 Selecta Mathematica. New Series
3 Algebra and Logic
3 Archiv der Mathematik
3 Bulletin of the London Mathematical Society
3 Illinois Journal of Mathematics
3 Publications Mathématiques
3 Journal für die Reine und Angewandte Mathematik
3 Mathematische Zeitschrift
3 Proceedings of the Edinburgh Mathematical Society. Series II
3 Discrete & Computational Geometry
3 Bulletin of the American Mathematical Society. New Series
3 Geometry & Topology
3 Advances in Geometry
3 Groups, Geometry, and Dynamics
3 Algebra & Number Theory
3 Journal of Logic and Analysis
3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
2 Discrete Mathematics
2 Journal of Mathematical Analysis and Applications
2 Mathematical Notes
2 Annales Polonici Mathematici
2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
2 Commentarii Mathematici Helvetici
2 Journal of Differential Equations
2 Journal of Number Theory
2 Mathematika
2 Proceedings of the London Mathematical Society. Third Series
2 Topology and its Applications
2 Journal of Complexity
2 Differential Geometry and its Applications
2 L’Enseignement Mathématique. 2e Série
2 Mémoires de la Société Mathématique de France. Nouvelle Série
2 Computational Complexity
2 Journal of Mathematical Sciences (New York)
2 Theory of Computing Systems
2 Algebraic & Geometric Topology
2 Foundations of Computational Mathematics
2 Journal of Algebra and its Applications
2 Logical Methods in Computer Science
2 Arnold Mathematical Journal
1 Archiv für Mathematische Logik und Grundlagenforschung
1 Communications in Algebra
1 Information Processing Letters
1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
1 Mathematical Proceedings of the Cambridge Philosophical Society
1 Acta Mathematica Vietnamica
1 Algebra Universalis
1 The Annals of Probability
1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Mathématiques
1 Canadian Mathematical Bulletin
1 Collectanea Mathematica
1 Fundamenta Mathematicae
1 Journal of Approximation Theory
1 Journal of Combinatorial Theory. Series B
1 Journal of Computational and Applied Mathematics
1 Journal of Graph Theory
1 Journal of the London Mathematical Society. Second Series
1 Journal of the Mathematical Society of Japan
1 Journal of Philosophical Logic
1 Manuscripta Mathematica
1 Mathematische Nachrichten
1 Mathematical Systems Theory
1 Memoirs of the American Mathematical Society
1 Pacific Journal of Mathematics
1 Rendiconti del Circolo Matemàtico di Palermo. Serie II
1 Siberian Mathematical Journal
1 Insurance Mathematics & Economics
1 Combinatorica
1 Acta Applicandae Mathematicae
1 Order
...and 39 more Serials
all top 5

Cited in 46 Fields

368 Mathematical logic and foundations (03-XX)
84 Algebraic geometry (14-XX)
78 Computer science (68-XX)
71 Number theory (11-XX)
69 Group theory and generalizations (20-XX)
56 Field theory and polynomials (12-XX)
56 Several complex variables and analytic spaces (32-XX)
29 Manifolds and cell complexes (57-XX)
26 Real functions (26-XX)
23 Combinatorics (05-XX)
18 Topological groups, Lie groups (22-XX)
17 Order, lattices, ordered algebraic structures (06-XX)
17 Functions of a complex variable (30-XX)
16 Differential geometry (53-XX)
14 Global analysis, analysis on manifolds (58-XX)
13 Commutative algebra (13-XX)
13 Dynamical systems and ergodic theory (37-XX)
11 Ordinary differential equations (34-XX)
8 General topology (54-XX)
7 Associative rings and algebras (16-XX)
7 Algebraic topology (55-XX)
6 Functional analysis (46-XX)
6 Geometry (51-XX)
5 General and overarching topics; collections (00-XX)
5 History and biography (01-XX)
5 Partial differential equations (35-XX)
5 Probability theory and stochastic processes (60-XX)
5 Numerical analysis (65-XX)
4 Approximations and expansions (41-XX)
4 Calculus of variations and optimal control; optimization (49-XX)
4 Information and communication theory, circuits (94-XX)
3 Special functions (33-XX)
3 Operator theory (47-XX)
3 Convex and discrete geometry (52-XX)
3 Statistical mechanics, structure of matter (82-XX)
3 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
2 Category theory; homological algebra (18-XX)
2 Measure and integration (28-XX)
2 Potential theory (31-XX)
2 Abstract harmonic analysis (43-XX)
2 Operations research, mathematical programming (90-XX)
2 Systems theory; control (93-XX)
1 General algebraic systems (08-XX)
1 Sequences, series, summability (40-XX)
1 Statistics (62-XX)
1 Biology and other natural sciences (92-XX)

Citations by Year

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