Lou van den Dries

1977 …2019
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Research Output 1977 2019

1977

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

1979

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

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

New decidable fields of algebraic numbers

Van Den Dries, L., Nov 1979, In : Proceedings of the American Mathematical Society. 77, 2, p. 251-256 6 p.

Research output: Contribution to journalArticle

Algebraic number
Closed
Subfield

Ultraproducts and approximation in local rings I

Becker, J., Denef, J., Lipshitz, L. & van den Dries, L., Jun 1 1979, In : Inventiones Mathematicae. 51, 2, p. 189-203 15 p.

Research output: Contribution to journalArticle

Ultraproduct
Local Ring
Approximation
1980
Elimination Theory
Real Closed Fields
Quantifier Elimination
Quantifiers
Linearly

Some model theory and number theory for models of weak systems of arithmetic

van den Dries, L., 1980, Model theory of algebra and arithmetic (Proc. Conf., Karpacz, 1979). Springer Berlin, Vol. 834. p. 346-362 17 p. (Lecture Notes in Math.).

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

1981

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

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

Quantifier elimination for linear formulas over ordered and valued fields

van den Dries, L., 1981, In : Bull. Soc. Math. Belg. Sér. B. 33, 1, p. 19-31 13 p.

Research output: Contribution to journalArticle

Subgroups of free profinite groups and large subfields of {Mathematical expression}

Lubotzky, A. & van den Dries, L., Mar 1 1981, In : Israel Journal of Mathematics. 39, 1-2, p. 25-45 21 p.

Research output: Contribution to journalArticle

Profinite Groups
Irreducibility
Subfield
Free Group
Hilbert
Polynomials
Ring
Curve
Axioms
Proof by induction
1982

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

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

Some applications of a model theoretic fact to (semi-) algebraic geometry

van den Dries, L., 1982, In : Indagationes Mathematicae (Proceedings). 85, 4, p. 397-401 5 p.

Research output: Contribution to journalArticle

Some applications of a model theoretic fact to (semi-) algebraic geometry

van den Dries, L., Dec 1 1982, In : Indagationes Mathematicae. 44, 4, p. 397-401 5 p.

Research output: Contribution to journalArticle

Algebraic Geometry
Model
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

Injective polynomial maps and the Jacobian conjecture

Connell, E. & van den Dries, L., Jun 1983, In : Journal of Pure and Applied Algebra. 28, 3, p. 235-239 5 p.

Research output: Contribution to journalArticle

Jacobian Conjecture
Polynomial Maps
Injective

Reducing to prime characteristic

van den Dries, L., 1983, Rijksuniversiteit Utrecht, Mathematical Institute, Utrecht. (Communications of the Mathematical Institute, Rijksuniversiteit Utrecht)

Research output: Book/ReportBook

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

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
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
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
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

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
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