16 found
Order:
  1.  31
    Dimension of definable sets, algebraic boundedness and Henselian fields.Lou Van den Dries - 1989 - Annals of Pure and Applied Logic 45 (2):189-209.
  2.  41
    Algebraic theories with definable Skolem functions.Lou van den Dries - 1984 - Journal of Symbolic Logic 49 (2):625-629.
  3.  45
    T-convexity and tame extensions II.Lou van den Dries - 1997 - Journal of Symbolic Logic 62 (1):14-34.
    I solve here some problems left open in “T-convexity and Tame Extensions” [9]. Familiarity with [9] is assumed, and I will freely use its notations. In particular,Twill denote a completeo-minimal theory extending RCF, the theory of real closed fields. Let (,V) ⊨Tconvex, let=V/m(V)be the residue field, with residue class mapx↦:V↦, and let υ:→ Γ be the associated valuation. “Definable” will mean “definable with parameters”.The main goal of this article is to determine the structure induced by(,V)on its residue fieldand on its (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   11 citations  
  4.  45
    On the structure of semialgebraic sets over p-adic fields.Philip Scowcroft & Lou van den Dries - 1988 - Journal of Symbolic Logic 53 (4):1138-1164.
  5.  28
    Logarithmic-exponential series.Lou van den Dries, Angus Macintyre & David Marker - 2001 - Annals of Pure and Applied Logic 111 (1-2):61-113.
    We extend the field of Laurent series over the reals in a canonical way to an ordered differential field of “logarithmic-exponential series” , which is equipped with a well behaved exponentiation. We show that the LE-series with derivative 0 are exactly the real constants, and we invert operators to show that each LE-series has a formal integral. We give evidence for the conjecture that the field of LE-series is a universal domain for ordered differential algebra in Hardy fields. We define (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  6.  45
    On the elementary theory of restricted elementary functions.Lou van den Dries - 1988 - Journal of Symbolic Logic 53 (3):796-808.
  7.  37
    Alfred Tarski's elimination theory for real closed fields.Lou Van Den Dries - 1988 - Journal of Symbolic Logic 53 (1):7-19.
  8.  46
    Quantifier elimination for modules with scalar variables.Lou van den Dries & Jan Holly - 1992 - Annals of Pure and Applied Logic 57 (2):161-179.
    Van den Dries, L. and J. Holly, Quantifier elimination for modules with scalar variables, Annals of Pure and Applied Logic 57 161–179. We consider modules as two-sorted structures with scalar variables ranging over the ring. We show that each formula in which all scalar variables are free is equivalent to a formula of a very simple form, uniformly and effectively for all torsion-free modules over gcd domains . For the case of Presburger arithmetic with scalar variables the result takes a (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  9.  51
    Toward a Model Theory for Transseries.Matthias Aschenbrenner, Lou van den Dries & Joris van der Hoeven - 2013 - Notre Dame Journal of Formal Logic 54 (3-4):279-310.
    The differential field of transseries extends the field of real Laurent series and occurs in various contexts: asymptotic expansions, analytic vector fields, and o-minimal structures, to name a few. We give an overview of the algebraic and model-theoretic aspects of this differential field and report on our efforts to understand its elementary theory.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10.  26
    University of California at Berkeley Berkeley, CA, USA March 24–27, 2011.G. Aldo Antonelli, Laurent Bienvenu, Lou van den Dries, Deirdre Haskell, Justin Moore, Christian Rosendal Uic, Neil Thapen & Simon Thomas - 2012 - Bulletin of Symbolic Logic 18 (2).
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  11.  11
    An application of tarskis principle to absolute Galois groups of function fields.Lou van den Dries & Paulo Ribenboim - 1987 - Annals of Pure and Applied Logic 33 (C):83-107.
  12.  38
    Correction to “T-convexity and tame extensions II”.Lou Van Den Dries - 1998 - Journal of Symbolic Logic 63 (4):1597-1597.
    Related Works: Original Paper: Lou Van Den Dries. $T$-Convexity and Tame Extensions II. J. Symbolic Logic, Volume 62, Issue 1 , 14--34. Project Euclid: euclid.jsl/1183745182.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  13.  37
    Definable equivalence relations on algebraically closed fields.Lou van den Dries, David Marker & Gary Martin - 1989 - Journal of Symbolic Logic 54 (3):928-935.
  14.  21
    Invariant measures on groups satisfying various chain conditions.Lou van den Dries & Vinicius Cifú Lopes - 2011 - Journal of Symbolic Logic 76 (1):209.
    For any group satisfying a suitable chain condition, we construct a finitely additive measure on it that is invariant under certain actions.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  15.  19
    The Euclidean algorithm on the natural numbers Æ= 0, 1,... can be specified succinctly by the recursive program.Lou Van Den Dries & Yiannis N. Moschovakis - 2004 - Bulletin of Symbolic Logic 10 (3):390-418.
    The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  16.  42
    Is The Euclidean Algorithm Optimal Among Its Peers?Lou Van Den Dries & Yiannis N. Moschovakis - 2004 - Bulletin of Symbolic Logic 10 (3):390-418.
    The Euclidean algorithm on the natural numbers ℕ = {0,1,…} can be specified succinctly by the recursive programwhere rem is the remainder in the division of a by b, the unique natural number r such that for some natural number q,It is an algorithm from the remainder function rem, meaning that in computing its time complexity function cε, we assume that the values rem are provided on demand by some “oracle” in one “time unit”. It is easy to prove thatMuch (...)
    Direct download (11 more)  
     
    Export citation  
     
    Bookmark