18 found
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  1.  30
    On the Scheme of Induction for Bounded Arithmetic Formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (3):261-302.
  2.  23
    Provability of the Pigeonhole Principle and the Existence of Infinitely Many Primes.J. B. Paris, A. J. Wilkie & A. R. Woods - 1988 - Journal of Symbolic Logic 53 (4):1235-1244.
  3.  10
    A Hierarchy of Cuts in Models of Arithmetic.J. B. Paris, L. Pacholski, J. Wierzejewski, A. J. Wilkie, George Mills & Jussi Ketonen - 1986 - Journal of Symbolic Logic 51 (4):1062-1066.
  4. The Laws of Integer Divisibility, and Solution Sets of Linear Divisibility Conditions.L.den Dries & A. J. Wilkie - 2003 - 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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  5.  38
    J. B. Paris. 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 L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture Notes in Mathematics, Vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, Pp. 312–337. - George Mills. 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. - Jussi Ketonen and Robert Solovay. Rapidly Growing Ramsey Functions. Annals of Mathematics, Ser. 2 Vol. 113 , Pp. 267–314. [REVIEW]A. J. Wilkie - 1986 - Journal of Symbolic Logic 51 (4):1062-1066.
  6.  44
    European Summer Meeting of the Association for Symbolic Logic, Manchester, England, 1984.P. Aczel, J. B. Paris, A. J. Wilkie, G. M. Wilmers & C. E. M. Yates - 1986 - Journal of Symbolic Logic 51 (2):480-502.
  7.  13
    Samuel R. Buss. Bounded Arithmetic. Studies in Proof Theory. Lecture Notes, No. 3. Bibliopolis, Naples1986, V + 221 Pp. [REVIEW]A. J. Wilkie - 1991 - Journal of Symbolic Logic 56 (2):759-760.
  8.  29
    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]A. J. Wilkie - 1986 - Journal of Symbolic Logic 51 (4):1062-1066.
  9.  24
    Classification of Quantifier Prefixes Over Exponential Diophantine Equations.J. P. Jones, H. Levitz & A. J. Wilkie - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (25-30):399-406.
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  10.  31
    Fusing O-Minimal Structures.A. J. Wilkie - 2005 - 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.  15
    The Laws of Integer Divisibility, and Solution Sets of Linear Divisibility Conditions.L. van den Dries & A. J. Wilkie - 2003 - 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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  12.  11
    Review: Samuel R. Buss, Bounded Arithmetic. [REVIEW]A. J. Wilkie - 1991 - Journal of Symbolic Logic 56 (2):759-760.
  13.  9
    Some Results and Problems on Complex Germs with Definable Mittag–Leffler Stars.A. J. Wilkie - 2013 - 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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  14.  13
    Diophantine Properties of Sets Definable in o-Minimal Structures.A. J. Wilkie - 2004 - Journal of Symbolic Logic 69 (3):851-861.
  15.  4
    On Defining $C^Infty$.A. J. Wilkie - 1994 - Journal of Symbolic Logic 59 (1):344-344.
  16.  20
    On Defining C∞.A. J. Wilkie - 1994 - Journal of Symbolic Logic 59 (1):344 -.
  17.  8
    Ramsey Quantifiers in Arithmetic.Angus Macintyre, L. Pacholski, J. Wierzejewski, A. J. Wilkie, James H. Schmerl & Stephen G. Simpson - 1985 - Journal of Symbolic Logic 50 (4):1078-1079.
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  18. Of Linear Divisibility Conditions.L. van Den Dries & A. J. Wilkie - unknown
    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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