Lou van den Dries

1977 …2019
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Research Output 1977 2019

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

Tame topology and o-minimal structures

van den Dries, L., 1998, Cambridge University Press, Cambridge. (London Mathematical Society Lecture Note Series)

Research output: Book/ReportBook

The real field with convergent generalized power series

van den Dries, L. & Speissegger, P., Dec 1 1998, In : Transactions of the American Mathematical Society. 350, 11, p. 4377-4421 45 p.

Research output: Contribution to journalArticle

Power series
O-minimal
Series
Model
1997

Logarithmic-exponential power series

van den Dries, L., Macintyre, A. & Marker, D., Dec 1997, In : Journal of the London Mathematical Society. 56, 3, p. 417-434 18 p.

Research output: Contribution to journalArticle

Power series
Logarithmic
Improper integral
Exponentiation
Riemann zeta function

T-convexity and Tame Extensions II

van den Dries, L., Mar 1997, In : Journal of Symbolic Logic. 62, 1, p. 14-34 21 p.

Research output: Contribution to journalArticle

Convexity
1996

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

o-minimal structures on the field of real numbers

van den Dries, L., 1996, In : Jahresber. Deutsch. Math.-Verein.. 98, 3, p. 165-171 7 p.

Research output: Contribution to journalArticle

1995

On the real exponential field with restricted analytic functions

van den Dries, L. & Miller, C., Feb 1 1995, In : Israel Journal of Mathematics. 92, 1-3, 1 p.

Research output: Contribution to journalComment/debate

Analytic function

Parametrizing the solutions of an analytic differential equation

van den Dries, L., 1995, In : Illinois Journal of Mathematics. 39, 3, p. 450-462 13 p.

Research output: Contribution to journalArticle

Differential equation
1994

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

On the real exponential field with restricted analytic functions

van den Dries, L. & Miller, C., Feb 1 1994, In : Israel Journal of Mathematics. 85, 1-3, p. 19-56 38 p.

Research output: Contribution to journalArticle

Analytic function
Cell Decomposition
O-minimal
Unary
Model

The elementary theory of restricted analytic fields with exponentiation

van den Dries, L., Macintyre, A. & Marker, D., 1994, In : Annals of Mathematics. 140, 1, p. 183-205 23 p.

Research output: Contribution to journalArticle

1993

On the integer zeros of exponential polynomials

Henson, C. W., Rubel, L. A., van den Dries, L. & Singer, M. F., 1993, In : Complex Variables Theory Appl.. 23, 3-4, p. 201-211 11 p.

Research output: Contribution to journalArticle

1992

Analytic Ax-Kochen-Ersov theorems

van den Dries, L., 1992, Proceedings of the International Conference on Algebra, Part 3 (Novosibirsk, 1989). Amer. Math. Soc., Providence, RI, Vol. 131. p. 379-398 20 p. (Contemp. Math.).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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

Quantifier elimination for modules with scalar variables

van den Dries, L. & Holly, J., May 25 1992, In : Annals of Pure and Applied Logic. 57, 2, p. 161-179 19 p.

Research output: Contribution to journalArticle

Quantifier Elimination
Scalar
Module
Torsion-free
Decidability
1991

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
1990

Surjective polynomial maps, and a remark on the jacobian problem

McKenna, K. & van den Dries, L., Dec 1 1990, In : Manuscripta Mathematica. 67, 1, p. 1-15 15 p.

Research output: Contribution to journalArticle

Polynomial Maps

The logic of Rumely's local-global principle

van den Dries, L. & Macintyre, A., Jan 1 1990, In : Journal fur die Reine und Angewandte Mathematik. 1990, 407, p. 33-56 24 p.

Research output: Contribution to journalArticle

Local-global Principle
Logic

Weil's group chunk theorem: a topological setting

van den Dries, L. P. D., 1990, In : Illinois Journal of Mathematics. 34, 1, p. 127-139 13 p.

Research output: Contribution to journalArticle

Well’s group chunk theorem: A topological setting

van den Dries, L., Jan 1 1990, In : Illinois Journal of Mathematics. 34, 1, p. 127-139 13 p.

Research output: Contribution to journalArticle

Theorem
1989

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

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

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
1988

$p$-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

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

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

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

On the elementary theory of restricted elementary functions

van den Dries, L., 1988, In : Journal of Symbolic Logic. 53, 3, p. 796-808 13 p.

Research output: Contribution to journalArticle

On the structure of semialgebraic sets over $p$-adic fields

Scowcroft, P. & van den Dries, L., 1988, In : Journal of Symbolic Logic. 53, 4, p. 1138-1164 27 p.

Research output: Contribution to journalArticle

1987

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
Theorem
Generalization

An application of Tarski's principle to absolute Galois groups of function fields

van den Dries, L. & Ribenboim, P., 1986, Algebra and order (Luminy-Marseille, 1984). Heldermann, Berlin, Vol. 14. p. 131-148 18 p. (Res. Exp. Math.).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

Real variables
Exponential functions
Brushes
Amplification
DNA

Tarski's problem and pfaffian functions

van den Dries, L., Jan 1986, In : Studies in Logic and the Foundations of Mathematics. 120, C, p. 59-90 32 p.

Research output: Contribution to journalArticle

Pfaffian
Semi-algebraic Sets
Finiteness
Cell
Logical property
1985

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

The field of reals with a predicate for the powers of two

van den Dries, L., Mar 1 1985, In : Manuscripta Mathematica. 54, 1-2, p. 187-195 9 p.

Research output: Contribution to journalArticle

Predicate
1984

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

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 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

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

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

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

On Skolem's exponential functions below $2^2^X$

van den Dries, L. & Levitz, H., 1984, In : Transactions of the American Mathematical Society. 286, 1, p. 339-349 11 p.

Research output: Contribution to journalArticle

On skolem’s exponential functions below 22

van den Dries, L. & Levitz, H., Jan 1 1984, In : Transactions of the American Mathematical Society. 286, 1, p. 339-349 11 p.

Research output: Contribution to journalArticle

Exponential functions
Multiplication
Identity function
Closed
Order Type

Remarks on Tarski's problem concerning (R, +, *, exp)

van den Dries, L., Jan 1 1984, In : Studies in Logic and the Foundations of Mathematics. 112, C, p. 97-121 25 p.

Research output: Contribution to journalArticle

Real Closed Fields
Decidability
Transcendental
Quantifiers
Elimination

The absolute Galois group of a rational function field in characteristic zero is a semidirect product

van den Dries, L. & Ribenboim, P., 1984, In : Canadian Mathematical Bulletin. 27, 3, p. 313-315 3 p.

Research output: Contribution to journalArticle

1983

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