Lou van den Dries

1977 …2019
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Research Output 1977 2019

$p$-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 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

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 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

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

An intermediate value property for first-order differential polynomials

van den Dries, L., 2000, Connections between model theory and algebraic and analytic geometry. Dept. Math., Seconda Univ. Napoli, Caserta, Vol. 6. p. 95-105 11 p. (Quad. Mat.).

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

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

Approximate groups [according to Hrushovski and Breuillard, Green, Tao]

van den Dries, L., Jan 1 2015, Asterisque. Société mathématique de France, p. 79-113 35 p. (Asterisque; vol. 367-368).

Research output: Chapter in Book/Report/Conference proceedingChapter

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

Asymptotic differential algebra

Aschenbrenner, M. & van den Dries, L., 2005, Analyzable functions and applications. Amer. Math. Soc., Providence, R.I., Vol. 373. p. 49-85 37 p. (Contemp. Math.).

Research output: Chapter in Book/Report/Conference proceedingChapter

Asymptotic differential algebra and model theory of transseries

Aschenbrenner, M., van den Dries, L. & van der Hoeven, J., 2017, Princeton University Press, Princeton, NJ. (Annals of Mathematics Studies)

Research output: Book/ReportBook

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

Classical model theory of fields

van den Dries, L., 2000, Model theory, algebra, and geometry. Cambridge Univ. Press, Cambridge, Vol. 39. p. 37-52 16 p. (Math. Sci. Res. Inst. Publ.).

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

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 in the realm of transseries

Aschenbrenner, M., van den Dries, L. & Van Der Hoeven, J., Jan 1 2017, Contemporary Mathematics. American Mathematical Society, p. 23-39 17 p. (Contemporary Mathematics; vol. 697).

Research output: Chapter in Book/Report/Conference proceedingChapter

Codimension
Subset
Term

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: Globalizing locally compact local groups (Journal of Lie Theory (2010) 20 (519-524))

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

Research output: Contribution to journalComment/debate

Locally Compact

Erratum to: Mann Pairs

van den Dries, L. & Günaydin, A., Mar 31 2011, In : Transactions of the American Mathematical Society. 363, 9, 1 p.

Research output: Contribution to journalComment/debate

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