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  1.  7
    A. J. Wilkie & J. B. Paris (1987). On the Scheme of Induction for Bounded Arithmetic Formulas. Annals of Pure and Applied Logic 35 (3):261-302.
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  2.  14
    J. B. Paris, A. J. Wilkie & A. R. Woods (1988). Provability of the Pigeonhole Principle and the Existence of Infinitely Many Primes. Journal of Symbolic Logic 53 (4):1235-1244.
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  3. L.den Dries & A. J. Wilkie (2003). The Laws of Integer Divisibility, and Solution Sets of Linear Divisibility Conditions. Journal of Symbolic Logic 68 (2):503 - 526.
    We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.
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  4.  1
    J. B. Paris, L. Pacholski, J. Wierzejewski, A. J. Wilkie, George Mills & Jussi Ketonen (1986). A Hierarchy of Cuts in Models of Arithmetic. Journal of Symbolic Logic 51 (4):1062-1066.
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  5.  14
    J. P. Jones, H. Levitz & A. J. Wilkie (1986). Classification of Quantifier Prefixes Over Exponential Diophantine Equations. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (25-30):399-406.
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  6.  9
    A. J. Wilkie (1994). On Defining C∞. Journal of Symbolic Logic 59 (1):344 -.
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  7.  10
    L. van den Dries & A. J. Wilkie (2003). The Laws of Integer Divisibility, and Solution Sets of Linear Divisibility Conditions. Journal of Symbolic Logic 68 (2):503-526.
    We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.
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  8.  1
    A. J. Wilkie (1986). Paris J. B.. A Hierarchy of Cuts in Models of Arithmetic. 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, Edited by Pacholski L., Wierzejewski J., and Wilkie A. J., Lecture Notes in Mathematics, Vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, Pp. 312–337.Mills George. A Tree Analysis of Unprovable Combinatorial Statements. 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, Pp. 248–311.Ketonen Jussi and Solovay Robert. Rapidly Growing Ramsey Functions. Annals of Mathematics, Ser. 2 Vol. 113 , Pp. 267–314. [REVIEW] Journal of Symbolic Logic 51 (4):1062-1066.
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  9.  16
    P. Aczel, J. B. Paris, A. J. Wilkie, G. M. Wilmers & C. E. M. Yates (1986). European Summer Meeting of the Association for Symbolic Logic: Manchester, England, 1984. Journal of Symbolic Logic 51 (2):480-502.
  10.  9
    A. J. Wilkie (2005). Fusing O-Minimal Structures. Journal of Symbolic Logic 70 (1):271 - 281.
    In this note I construct a proper o-minimal expansion of the ordered additive group of rationals.
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  11.  11
    A. J. Wilkie (2004). Diophantine Properties of Sets Definable in o-Minimal Structures. Journal of Symbolic Logic 69 (3):851-861.
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  12.  3
    A. J. Wilkie (1986). 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. [REVIEW] Journal of Symbolic Logic 51 (4):1062-1066.
  13.  3
    J. P. Jones, H. Levitz & A. J. Wilkie (1986). Classification of Quantifier Prefixes Over Exponential Diophantine Equations. Mathematical Logic Quarterly 32 (25‐30):399-406.
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  14.  3
    A. J. Wilkie (2013). Some Results and Problems on Complex Germs with Definable Mittag–Leffler Stars. Notre Dame Journal of Formal Logic 54 (3-4):603-610.
    Working in an o-minimal expansion of the real field, we investigate when a germ of a complex analytic function has a definable analytic continuation to its Mittag–Leffler star. As an application we show that any algebro-logarithmic function that is complex analytic in a neighborhood of the origin in $\mathbb {C}$ has an analytic continuation to all but finitely many points in $\mathbb {C}$.
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  15.  1
    A. J. Wilkie (1994). On Defining $C^Infty$. Journal of Symbolic Logic 59 (1):344-344.
  16. L. van Den Dries & A. J. Wilkie, Of Linear Divisibility Conditions.
    We prove linear and polynomial growth properties of sets and functions that are existentially definable in the ordered group of integers with divisibility. We determine the laws of addition with order and divisibility.
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  17. P. Aczel, J. B. Paris, A. J. Wilkie, G. M. Wilmers & C. E. M. Yates (1986). European Summer Meeting of the Association for Symbolic Logic, Manchester, England, 1984. Journal of Symbolic Logic 51 (2):480-502.
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  18. J. B. Paris, A. J. Wilkie, G. M. Wilmers & Association for Symbolic Logic (1986). Logic Colloquium '84 Proceedings of the Colloquium Held in Manchester, U.K., July 1984. Monograph Collection (Matt - Pseudo).
     
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  19. Shih Ping Tung, Charles N. Delzell, J. P. Jones, H. Levitz & A. J. Wilkie (1988). Note on Quantifier Prefixes Over Diophantine Equations.Classification of Quantifier Prefixes Over Exponential Diophantine Equations. Journal of Symbolic Logic 53 (1):309.
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  20. A. J. Wilkie (1991). Buss Samuel R.. Bounded Arithmetic. Studies in Proof Theory. Lecture Notes, No. 3. Bibliopolis, Naples 1986, V + 221 Pp. [REVIEW] Journal of Symbolic Logic 56 (2):759-760.
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  21. A. J. Wilkie (1991). Review: Samuel R. Buss, Bounded Arithmetic. [REVIEW] Journal of Symbolic Logic 56 (2):759-760.
  22. A. J. Wilkie (2013). Some Results and Problems on Complex Germs with Definable Mittag–Leffler Stars. Notre Dame Journal of Formal Logic 54 (3-4):603-610.
    Working in an o-minimal expansion of the real field, we investigate when a germ of a complex analytic function has a definable analytic continuation to its Mittag–Leffler star. As an application we show that any algebro-logarithmic function that is complex analytic in a neighborhood of the origin in $\mathbb {C}$ has an analytic continuation to all but finitely many points in $\mathbb {C}$.
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