Works by A. J. Wilkie

( view other items matching `A. J. Wilkie`, view all matches )
13 found
Order:
  1.  71
    On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   97 citations  
  2.  58
    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.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   28 citations  
  3.  248
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  4.  102
    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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  5.  62
    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.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  6.  41
    Classification of Quantifier Prefixes Over Exponential Diophantine Equations.J. P. Jones, H. Levitz & A. J. Wilkie - 1986 - Mathematical Logic Quarterly 32 (25-30):399-406.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  7. 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.
     
    Export citation  
     
    Bookmark  
  8.  50
    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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  9.  44
    Diophantine properties of sets definable in o-minimal structures.A. J. Wilkie - 2004 - Journal of Symbolic Logic 69 (3):851-861.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark  
  10.  47
    On defining c∞.A. J. Wilkie - 1994 - Journal of Symbolic Logic 59 (1):344 -.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  11.  33
    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 $\mathbb {C}$.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark  
  12.  134
    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.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  13.  51
    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.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark