Lou van den Dries

1977 …2019
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Research Output 1977 2019

2019

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

Logarithmic hyperseries

van den Dries, L., van der Hoeven, J. & Kaplan, E., Jul 1 2019, In : Transactions of the American Mathematical Society. 372, 7, p. 5199-5241 43 p.

Research output: Contribution to journalArticle

Logarithmic
Chemical analysis

On the uniqueness of maximal immediate extensions of valued differential fields

van den Dries, L. & Pynn-Coates, N., Feb 1 2019, In : Journal of Algebra. 519, p. 87-100 14 p.

Research output: Contribution to journalArticle

Uniqueness
Field extension
Monotonicity
Union
Existence and Uniqueness

The surreal numbers as a universal H-field

Aschenbrenner, M., van den Dries, L. & Van Der Hoeven, J., Jan 1 2019, In : Journal of the European Mathematical Society. 21, 4, p. 1179-1199 21 p.

Research output: Contribution to journalArticle

2018

Maximal immediate extensions of valued differential fields

Aschenbrenner, M., van den Dries, L. & van der Hoeven, J., Aug 2018, In : Proceedings of the London Mathematical Society. 117, 2, p. 376-406 31 p.

Research output: Contribution to journalArticle

Isomorphism
Uniqueness
2017

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

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
2016

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

2015

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

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

2014

Lectures on the model theory of valued fields

van den Dries, L., Jan 1 2014, In : Lecture Notes in Mathematics. 2111, p. 55-157 103 p.

Research output: Contribution to journalArticle

Valued Fields
Model Theory

Model theory in algebra, analysis and arithmetic

van den Dries, L., Koenigsmann, J., Macpherson, H. D., Pillay, A., Toffalori, C. & Wilkie, A. J., 2014, Springer, Heidelberg; Centro Internazionale Matematico Estivo (C.I.M.E.), Florence. (Lecture Notes in Mathematics)

Research output: Book/ReportBook

Truncation in Hahn fields

van den Dries, L., 2014, Valuation theory in interaction. Eur. Math. Soc., Zürich, p. 579-595 17 p. (EMS Ser. Congr. Rep.).

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

2013

Toward a model theory for transseries

Aschenbrenner, M., Van Den Dries, L. & Van Der Hoeven, J., Oct 10 2013, In : Notre Dame Journal of Formal Logic. 54, 3-4, p. 279-310 32 p.

Research output: Contribution to journalArticle

Model Theory
O-minimal Structures
Laurent Series
Asymptotic Expansion
Vector Field
2012

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 ``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

2011

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

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

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

Invariant measures on groups satisfying various chain conditions

Van Den Dries, L. & Vinicius, C. L., Mar 1 2011, In : Journal of Symbolic Logic. 76, 1, p. 209-226 18 p.

Research output: Contribution to journalArticle

Finitely Additive Measure
Chain Condition
Invariant Measure
Invariant
2010

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

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

Mann pairs

van den Dries, L. & Günaydin, A., May 1 2010, In : Transactions of the American Mathematical Society. 362, 5, p. 2393-2414 22 p.

Research output: Contribution to journalArticle

Roots of Unity
Field extension
Finite Set
Multiplicative
Arbitrary

Triangulation in o-minimal fields with standard part map

van den Dries, L. & Maříková, J., Dec 1 2010, In : Fundamenta Mathematicae. 209, 2, p. 133-155 23 p.

Research output: Contribution to journalArticle

O-minimal
Triangulation
Question Answering
Subring
Standards
2009

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

Locally compact contractive local groups

van den Dries, L. & Goldbring, I., 2009, In : Journal of Lie Theory. 19, 4, p. 685-695 11 p.

Research output: Contribution to journalArticle

Locally Compact
Locally Connected
Structure Theorem
Automorphism
Isomorphic
2008

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

Isomorphism of complete local noetherian rings and strong approximation

van den Dries, L., Oct 1 2008, In : Proceedings of the American Mathematical Society. 136, 10, p. 3435-3448 14 p.

Research output: Contribution to journalArticle

Strong Approximation
Noetherian Ring
Local Ring
Isomorphism
Isomorphic
2006

On explicit definability in arithmetic

van den Dries, L., 2006, Logic in Tehran. Assoc. Symbol. Logic, La Jolla, CA, Vol. 26. p. 65-86 22 p. (Lect. Notes Log.).

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

The fields of real and complex numbers with a small multiplicative group

van den Dries, L. & Günaydin, A., Jul 2006, In : Proceedings of the London Mathematical Society. 93, 1, p. 43-81 39 p.

Research output: Contribution to journalArticle

Complex number
Multiplicative
2005

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

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

Liouville closed H-fields

Aschenbrenner, M. & van den Dries, L., May 1 2005, In : Journal of Pure and Applied Algebra. 197, 1-3, p. 83-139 57 p.

Research output: Contribution to journalArticle

Closed
Location of Zeros
Differential Polynomial
Undecidability
Field extension
2004

The Euclidean algorithm optimal among its peers?

van den Dries, L. & Moschovakis, Y. N., Sep 1 2004, In : Bulletin of Symbolic Logic. 10, 3, p. 390-418 29 p.

Research output: Contribution to journalArticle

Euclidean algorithm
Peers
2003
Highest common factor
Recursive Algorithm
Integer
Divisor Function
Transcendental

The laws of integer divisibility, and solution sets of linear divisibility conditions

van den Dries, L. & Wilkie, A. J., Jun 2003, In : Journal of Symbolic Logic. 68, 2, p. 503-526 24 p.

Research output: Contribution to journalArticle

Divisibility
Solution Set
Ordered Group
Property of set
Integer
2002

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

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

Images of additive polynomials in double-struck F signq((t)) have the optimal approximation property

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

Research output: Contribution to journalArticle

Optimal Approximation
Approximation Property
Polynomial
Laurent Series
Several Variables

O-minimal preparation theorems

van den Dries, L. & Speissegger, P., 2002, Model theory and applications. Aracne, Rome, Vol. 11. p. 87-116 30 p. (Quad. Mat.).

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

2001

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

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

Logarithmic-exponential series

van den Dries, L., MacIntyre, A. & Marker, D., Jul 20 2001, In : Annals of Pure and Applied Logic. 111, 1-2, p. 61-113 53 p.

Research output: Contribution to journalArticle

Logarithmic
Series
Differential Algebra
Laurent Series
Invert
2000

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

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

The field of reals with multisummable series and the exponential function

van den Dries, L. & Speissegger, P., Nov 2000, In : Proceedings of the London Mathematical Society. 81, 3, p. 513-565 53 p.

Research output: Contribution to journalArticle

Series
1999

o-minimal structures and real analytic geometry

van den Dries, L., 1999, Current developments in mathematics, 1998 (Cambridge, MA). Int. Press, Somerville, MA, p. 105-152 48 p.

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

One-dimensional p-adic subanalytic sets

van den Dries, L., Haskell, D. & Macpherson, D., Feb 1999, In : Journal of the London Mathematical Society. 59, 1, p. 1-20 20 p.

Research output: Contribution to journalArticle

P-adic
Witt Vectors
Multiplicative
Ring
Invariant