Lou van den Dries

1977 …2019
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Research Output 1977 2019

Article

$p$-adic and real subanalytic sets

Denef, J. & van den Dries, L., 1988, In : Annals of Mathematics. 128, 1, p. 79-138 60 p.

Research output: Contribution to journalArticle

Theorem
Generalization

Alfred Tarski's elimination theory for real closed fields

van den Dries, L., 1988, In : Journal of Symbolic Logic. 53, 1, p. 7-19 13 p.

Research output: Contribution to journalArticle

Algebraic theories with definable Skolem functions

van den Dries, L., 1984, In : Journal of Symbolic Logic. 49, 2, p. 625-629 5 p.

Research output: Contribution to journalArticle

Algorithms and Bounds for Polynomial Rings

van den Dries, L., Jan 1 1979, In : Studies in Logic and the Foundations of Mathematics. 97, C, p. 147-157 11 p.

Research output: Contribution to journalArticle

Polynomial ring
Lemma
Intersection Theorem
Primitive Element
Express
Elimination Theory
Real Closed Fields
Quantifier Elimination
Quantifiers
Linearly

Analytic Hardy fields and exponential curves in the real plane

van den Dries, L., 1984, In : American Journal of Mathematics. 106, 1, p. 149-167 19 p.

Research output: Contribution to journalArticle

An application of tarskis principle to absolute Galois groups of function fields

van den Dries, L. & Ribenboim, P., 1987, In : Annals of Pure and Applied Logic. 33, C, p. 83-107 25 p.

Research output: Contribution to journalArticle

Galois group
Function Fields

An effective bound for groups of linear growth

Wilkie, A. J. & van den Dries, L., May 1 1984, In : Archiv der Mathematik. 42, 5, p. 391-396 6 p.

Research output: Contribution to journalArticle

A Polish group without Lie sums

van den Dries, L. & Gao, S., Jun 1 2009, In : Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg. 79, 1, p. 135-147 13 p.

Research output: Contribution to journalArticle

Polish Group
Lie Brackets
Invariant Metric
Free Group
Generator

Application de la théorie des modèles aux groupes de Galois de corps de fonctions

van den Dries, L. & Ribenboim, P., 1979, In : C. R. Acad. Sci. Paris Sér. A-B. 288, 17, p. A789-A792

Research output: Contribution to journalArticle

A remark on Ax's theorem on solvability modulo primes

van den Dries, L., Dec 1 1991, In : Mathematische Zeitschrift. 208, 1, p. 65-70 6 p.

Research output: Contribution to journalArticle

Solvability
Modulo
Theorem

Arithmetic complexity

Van Den Dries, L. & Moschovakis, Y. N., Nov 1 2008, In : ACM Transactions on Computational Logic. 10, 1, 2.

Research output: Contribution to journalArticle

Number theory
Lower bound
Arithmetic Functions
Highest common factor
Computing

Artin-Schreier theory for commutative regular rings

van den Dries, L., Dec 1977, In : Annals of Mathematical Logic. 12, 2, p. 113-150 38 p.

Research output: Contribution to journalArticle

A specialization theorem for analytic functions on compact sets

van den Dries, L., Dec 1 1982, In : Indagationes Mathematicae. 44, 4, p. 391-396 6 p.

Research output: Contribution to journalArticle

Specialization
Compact Set
Analytic function
Algebraic function
Theorem

A specialization theorem for analytic functions on compact sets

van den Dries, L., 1982, In : Indagationes Mathematicae (Proceedings). 85, 4, p. 391-396 6 p.

Research output: Contribution to journalArticle

Specialization
Compact Set
Analytic function
Algebraic function
Theorem

A specialization theorem for p-adic power series converging on the closed unit disc

van den Dries, L., Dec 1981, In : Journal of Algebra. 73, 2, p. 613-623 11 p.

Research output: Contribution to journalArticle

Specialization
P-adic
Power series
Unit Disk
Closed

Bounded pregeometries and pairs of fields

Ángel, L. & van den Dries, L., 2016, In : South American Journal of Logic. 2, 2, p. 459-475 17 p.

Research output: Contribution to journalArticle

Bounds in the theory of polynomial rings over fields. A nonstandard approach

van den Dries, L. & Schmidt, K., Feb 1 1984, In : Inventiones Mathematicae. 76, 1, p. 77-91 15 p.

Research output: Contribution to journalArticle

Polynomial ring

Closed Asymptotic Couples

Aschenbrenner, M. & Van Den Dries, L., Jan 1 2000, In : Journal of Algebra. 225, 1, p. 309-358 50 p.

Research output: Contribution to journalArticle

Closed
Vector space
Elimination Theory
Ordered Vector Space
Finitely Generated

Convergent Series Expansions of a New Type for Exponential Functions

van den Dries, L., 1989, In : Mathematische Nachrichten. 142, 1, p. 7-18 12 p.

Research output: Contribution to journalArticle

Series Expansion

Decidability and undecidability theorems for pac-fields

Cherlin, G., Van Den Dries, L. & Macintyre, A., Jan 1 1981, In : Bulletin of the American Mathematical Society. 4, 1, p. 101-104 4 p.

Research output: Contribution to journalArticle

Computability and decidability
Undecidability
Decidability
Theorem

Decidable regularly closed fields of algebraic numbers

van den Dries, L. & Smith, R. L., 1985, In : Journal of Symbolic Logic. 50, 2, p. 468-475 8 p.

Research output: Contribution to journalArticle

Definable equivalence relations on algebraically closed fields

van den Dries, L., Marker, D. & Martin, G., 1989, In : Journal of Symbolic Logic. 54, 3, p. 928-935 8 p.

Research output: Contribution to journalArticle

Definable sets in Mann pairs

van den Dries, L. & Günaydin, A., Aug 1 2011, In : Communications in Algebra. 39, 8, p. 2752-2763 12 p.

Research output: Contribution to journalArticle

Subfield
Algebraically closed
Multiplicative
Subgroup
First-order

Definable sets over finite fields

Chatzidakis, Z., van den Dries, L. & Macintyre, A., Jan 1 1992, In : Journal fur die Reine und Angewandte Mathematik. 1992, 427, p. 107-136 30 p.

Research output: Contribution to journalArticle

Galois field

Dense pairs of o-minimal structures

van den Dries, L., Dec 1 1998, In : Fundamenta Mathematicae. 157, 1, p. 61-78 18 p.

Research output: Contribution to journalArticle

O-minimal Structures
O-minimal
Ordered Group
Abelian group

Differentially algebraic gaps

Aschenbrenner, M., Van Den Dries, L. & Van Der Hoeven, J., Jun 1 2005, In : Selecta Mathematica, New Series. 11, 2, p. 247-280 34 p.

Research output: Contribution to journalArticle

differential equations
logarithms
Field extension
First order differential equation
Linear differential equation

Dimension of definable sets, algebraic boundedness and Henselian fields

Van den Dries, L., Dec 12 1989, In : Annals of Pure and Applied Logic. 45, 2 PART 1, p. 189-209 21 p.

Research output: Contribution to journalArticle

Algebraic Set
Boundedness

Division rings whose vector spaces are pseudofinite

van den Dries, L. & Lopes, V. C., Sep 1 2010, In : Journal of Symbolic Logic. 75, 3, p. 1087-1090 4 p.

Research output: Contribution to journalArticle

Division ring or skew field
Vector space
Thompson's Group
Axiomatization
First-order

Elementary equivalence and codimension in p-adic fields

Bélair, L., van den Dries, L. & Macintyre, A., Jun 1 1988, In : Manuscripta Mathematica. 62, 2, p. 219-225 7 p.

Research output: Contribution to journalArticle

P-adic Fields
Codimension
Equivalence
P-adic numbers
Subfield

Elementary equivalence and the commutator subgroup

van den Dries, L. P. D., Glass, A. M. W., Macintyre, A., Mekler, A. H. & Poland, J., Jul 1982, In : Glasgow Mathematical Journal. 23, 2, p. 115-117 3 p.

Research output: Contribution to journalArticle

Commutator subgroup
Equivalence

Elementary theory of valued fields with a valuation-preserving automorphism

Azgin, S. & Van Den Dries, L., Jan 1 2011, In : Journal of the Institute of Mathematics of Jussieu. 10, 1, p. 1-35 35 p.

Research output: Contribution to journalArticle

Valued Fields
Automorphism
Valuation
Model
Object

Elimination of quantifiers in algebraic structures

Macintyre, A., McKenna, K. & van den Dries, L., Jan 1983, In : Advances in Mathematics. 47, 1, p. 74-87 14 p.

Research output: Contribution to journalArticle

Quantifiers
Algebraic Structure
Elimination

Elimination theory for the ring of algebraic integers

van den Dries, L., Jan 1 1988, In : Journal fur die Reine und Angewandte Mathematik. 1988, 388, p. 189-205 17 p.

Research output: Contribution to journalArticle

Elimination Theory
Algebraic integer
Ring

Erratum to: ``Fields of surreal numbers and exponentiation''

van den Dries, L. & Ehrlich, P., 2001, In : Fundamenta Mathematicae. 168, 3, p. 295-297 3 p.

Research output: Contribution to journalArticle

Erratum to ``Globalizing locally compact local groups'' [MR2743102]

van den Dries, L. & Goldbring, I., 2012, In : Journal of Lie Theory. 22, 2, p. 489-490 2 p.

Research output: Contribution to journalArticle

Exponential rings, exponential polynomials and exponential functions

Van Den Dries, L., Jul 1984, In : Pacific Journal of Mathematics. 113, 1, p. 51-66 16 p.

Research output: Contribution to journalArticle

Exponential Polynomial
Polynomial function
Ring

Extending Tamm's theorem

van den Dries, L. & Miller, C., 1994, In : Annales de l'Institut Fourier. 44, 5, p. 1367-1395 29 p.

Research output: Contribution to journalArticle

Fields of surreal numbers and exponentiation

van den Dries, L. & Ehrlich, P., Jan 1 2001, In : Fundamenta Mathematicae. 167, 2, p. 173-188 16 p.

Research output: Contribution to journalArticle

Exponentiation
Subfield
Logarithm
If and only if
Closed
Highest common factor
Recursive Algorithm
Integer
Divisor Function
Transcendental

Geometric categories and O-minimal structures

Van Den Dries, L. & Miller, C., Aug 1 1996, In : Duke Mathematical Journal. 84, 2, p. 497-540 44 p.

Research output: Contribution to journalArticle

O-minimal Structures

Globalizing locally compact local groups

van den Dries, L. & Goldbring, I., 2010, In : Journal of Lie Theory. 20, 3, p. 519-524 6 p.

Research output: Contribution to journalArticle

Topological group
Locally Compact
Isomorphic

Gromov's theorem on groups of polynomial growth and elementary logic

van den Dries, L. & Wilkie, A. J., Aug 1984, In : Journal of Algebra. 89, 2, p. 349-374 26 p.

Research output: Contribution to journalArticle

Polynomial Growth
Logic
Theorem

H-fields and their Liouville extensions

Aschenbrenner, M. & Van Den Dries, L., Dec 1 2002, In : Mathematische Zeitschrift. 242, 3, p. 543-588 46 p.

Research output: Contribution to journalArticle

Model Theory
Logarithmic
Closure
Series

Hilbert's 5th problem

van den Dries, L. & Goldbring, I., 2015, In : Enseign. Math. (2). 61, 1-2, p. 3-43 41 p.

Research output: Contribution to journalArticle

Homogeneous universal H-fields

Van Den Dries, L., Ehrlich, P. & Mildenberger, H., May 2019, In : Proceedings of the American Mathematical Society. 147, 5, p. 2231-2234 4 p.

Research output: Contribution to journalArticle

Isomorphism
Model

Images of additive polynomials in $Bbb F_q((t))$ have the optimal approximation property

van den Dries, L. & Kuhlmann, F-V., 2002, In : Canadian Mathematical Bulletin. 45, 1, p. 71-79 9 p.

Research output: Contribution to journalArticle