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| Full name: | Alex Wilkie | Affiliation: | Mathematical Institute |
| University of Oxford | |||
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Address:
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24-29 St Giles | Phone: | (+44)(0) 1865 273540 |
| Oxford, OX1 3LB | Fax: | (+44)(0) 1865 273583 | |
| United Kingdom | email: | wilkie@maths.ox.ac.uk | |
Research |
1. On models of arithmetic-answers to two problems raised by H. Gaifman, J Symb Logic,40(1975)(1),41-47.
2. A note on products of finite structures with an application to graphs, J Lond Math Soc (2),14(1976),383-384.
3. On the theory of end-extensions of models of arithmetic,in:Set Theory and Hierarchy Theory V,SLNM 619,Springer-Verlag,1997,305-310.
4. On models of arithmetic having non-modular substructure lattices,Fund. Math.,XCV(1977),223-237.
5. Reconstruction theorems for families of sets (with R Rado),J Lond Math Soc (2),17(1978),5-9.
6. Applications of complexity theory to sigma-zero definability problems in arithmetic,in:Model Theory of Algebra and Arithmetic,SLNM 834, Springer-Verlag,1980,363-369.
7. Some results and problems on weak systems of arithmetic,in:Logic Colloquium '77,North-Holland,1980,285-296.
8. Models of arithmetic and the rudimentary sets (with J B Paris), Bull Soc Math Belg 33 (1981),1,157-169.
9. On discretely ordered rings in which every definable ideal is principal, in:Model Theory and Arithmetic,SLNM 890,Springer-Verlag,1981,297-303.
10. On core structures for Peano arithmetic,in:Logic Colloquium '80, North-Holland,1982,311-314.
11. Delta-zero sets and induction (with J B Paris),in:Open Days in Model Theory and Set Theory,Leeds University,1983,237-248.
12. Gromov's theorem on groups of polynomial growth and elementary logic (with L van den Dries),J Algebra,89 (1984),391-396.
13. An effective bound for groups of linear growth (with L van den Dries), Arch Math,42 (1984),391-396.
14. Counting problems in bounded arithmetic (with J B Paris),in:Methods in Mathematical logic,SLNM 1130,Springer-Verlag,1985,317-340.
15. Characterizing some low arithmetic classes (with J B Paris and W G Handley),Coll Math Soc Janos Bolyai,44 (1984),353-364.
16. Modeles non-standard en arithmetique et theorie des ensembles (with J-P Ressayre),Pub Math de l'universite Paris VII,1986,(147 pages).
17. On sentences interpretable in systems of arithmetic,in: Logic Colloquium '84,North-Holland,1986,329-342.
18. Classification of quantifier prefixes over exponential diophantine equations (with J P Jones and H Levitz),Z fur Math Log und Grund der Math,32 (1986),388-406.
19. Counting delta-zero sets (with J B Paris),Fund Math,127 (1) (1986), 67-76.
20. On the scheme of induction for bounded arithmetic formulas (with J B Paris),Annals of Pure and Applied Logic,35 (1987),261-302.
21. On schemes axiomatizing arithmetic,in:Proc of ICM,Berkeley,Ca,USA, 1986 (1988),331-337.
22. Provability of the Pigeonhole principle and the existence of infinitely many primes (with J B Paris and A R Woods),J Symb Logic, 53,(1988),12355-1244.
23. On the theory of the real exponential field,Illinois J Math,33,3,(1989), 384-408.
24. On the existence of end extensions of models of bounded induction,in: Logic,Methodology and Philosophy of Science,VIII (Moscow 1987),Stud Logic and Found Math,126,North Holland,1989,143-161.
25. On defining C-infinity,J Symb Logic,59,(1994),(1),344.
26. Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function,J Amer Math Soc,9,(4),1996,1051-1094.
27. On the decidability of the real exponential field (with A J Macintyre), in:Kreiseliana.About and Around Georg Kreisel',A K Peters,1996,441-467.
28. Schanuel's conjecture and the decidability of the real exponential field,in:Algebraic Model Theory,1997,Kluwer,223-230.
29. O-minimality,in:Proceedings of the ICM,Berlin,1998,Vol 1,Documenta Mathematica,J.DMV,1998,633-636.
30. Model theory of analytic and smooth functions,in:Models and Computability, LMS Lecture Notes Series 259,CUP,1999,407-419.
31. A theorem of the complement and some new O-minimal structures, Selecta Mathematica,New Ser.5 (1999),397-421.
32. On exponentiation - a solution to Tarski's High School Algebra Problem, in: Connections between Model Theory and Algebraic and Analytic Geometry, Quaderni di Matematica, vol. 6 (ed. by Angus Macintyre), Naples, 2000, 107-129. (dvi file, postscript file)
33. Quasianalytic Denjoy-Carleman classes and o-minimality (with J-P Rolin and P Speissegger), J Amer Math Soc,16,(2003),(4),751-777. (see http://www.math.wisc.edu/~speisseg/preprints/quasi.ps).
34. The laws of integer divisibility and solution sets of linear divisibilty conditions (with L van den Dries), J Symb Logic,68,(2003),(2),503-526. (postscript file)
35. Diophantine properties of sets definable in o-minimal structures, J Symb Logic,69,(2004),(3),851-861. (dvi file)
36. Fusing o-minimal structures, J Symb Logic,70, Number 1, March 2005, 271-281 (dvi file)
37. Covering definable open sets by open cells, Proceedings of the RAAG Summer School Lisbon 2003: O-minimal structures, Eds M. Edmundo, D. Richardson, A.J. Wilkie (2005), 77-103 (dvi file)
38. Liouville functions, Lecture Notes in Logic 19, Logic Colloquium 2000, Eds R. Cori, A. Razborov, S. Tudorcevic, C. Wood (2005), 383-391 (dvi file)
1. Back-and-forth with height and degree through the complex field, Oxford 2003.
2. Lecture notes on Marker's lecture notes on Ax's Theorem, Logic Advanced Class, Oxford 2003.
3. A remark on Schanuel's conjecture, Logic Advanced Class, Oxford 2003.
4. Further remarks on Schanuel's conjecture, Logic Advanced Class, Oxford 2003.