## van den Dries, Lou

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 Author ID: van-den-dries.lou Published as: van den Dries, Lou; Van den Dries, Lou; van den Dries, L. P. D.; van den Dries, L. more...less External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 113 Publications since 1977, including 3 Books 1 Further Contribution Co-Authors: 42 Co-Authors with 69 Joint Publications 741 Co-Co-Authors
all top 5

### Co-Authors

 43 single-authored 11 Aschenbrenner, Matthias 9 Macintyre, Angus John 8 van der Hoeven, Joris 4 Goldbring, Isaac 4 Günaydın, Ayhan 4 Marker, David E. 4 Miller, Chris 4 Ribenboim, Paulo 4 Wilkie, Alex James 3 Speissegger, Patrick 2 Denef, Jan 2 Ehrlich, Philip 2 Henson, C. Ward 2 Lopes, Vinicius Cifú 2 Moschovakis, Yiannis Nicholas 2 Rubel, Lee Albert 2 Singer, Michael F. 1 Azgin, Salih 1 Becker, Joseph A. 1 Bélair, Luc 1 Chatzidakis, Zoé Maria 1 Cherlin, Gregory L. 1 Connell, Edwin H. 1 Gao, Su 1 Glass, Andrew M. W. 1 Haskell, Deirdre 1 Holly, Jan E. 1 Kaplan, Elliot 1 Koenigsmann, Jochen 1 Kuhlmann, Franz-Viktor 1 Levitz, Hilbert 1 Lewenberg, Adam H. 1 Lipshitz, Leonard 1 Lubotzky, Alexander 1 Macpherson, Dugald 1 Macpherson, Hugh Dugald 1 Maříková, Jana 1 McKenna, Ken 1 McKenna, Kenneth 1 Mekler, Alan H. 1 Pillay, Anand 1 Poland, John C. 1 Pynn-Coates, Nigel 1 Scowcroft, Philip 1 Smith, Rick L. 1 Strooker, Jan Rustom 1 Toffalori, Carlo
all top 5

### Serials

 12 The Journal of Symbolic Logic 6 Transactions of the American Mathematical Society 5 Proceedings of the American Mathematical Society 4 Journal of Algebra 4 Manuscripta Mathematica 4 Annals of Pure and Applied Logic 3 Israel Journal of Mathematics 3 Fundamenta Mathematicae 3 Journal für die Reine und Angewandte Mathematik 3 Proceedings of the London Mathematical Society. Third Series 3 Journal of Lie Theory 2 Canadian Mathematical Bulletin 2 Illinois Journal of Mathematics 2 Indagationes Mathematicae 2 Inventiones Mathematicae 2 Journal of the London Mathematical Society. Second Series 2 Journal of Pure and Applied Algebra 2 Mathematische Zeitschrift 2 Bulletin of the American Mathematical Society. New Series 2 Annals of Mathematics. Second Series 1 Communications in Algebra 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Advances in Mathematics 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Annals of Mathematical Logic 1 Archiv der Mathematik 1 Duke Mathematical Journal 1 Glasgow Mathematical Journal 1 Mathematische Nachrichten 1 Notre Dame Journal of Formal Logic 1 Pacific Journal of Mathematics 1 Bulletin de la Société Matheḿatique de Belgique. Série B 1 Complex Variables. Theory and Application 1 L’Enseignement Mathématique. 2e Série 1 Selecta Mathematica. New Series 1 The Bulletin of Symbolic Logic 1 Journal of the European Mathematical Society (JEMS) 1 Foundations of Computational Mathematics 1 Journal of the Institute of Mathematics of Jussieu 1 ACM Transactions on Computational Logic 1 Comptes Rendus Hebdomadaires des Séances de l’Académie des Sciences, Série A 1 Annals of Mathematics Studies 1 Lecture Notes in Mathematics 1 London Mathematical Society Lecture Note Series
all top 5

### Fields

 84 Mathematical logic and foundations (03-XX) 61 Field theory and polynomials (12-XX) 21 Number theory (11-XX) 21 Algebraic geometry (14-XX) 18 Commutative algebra (13-XX) 11 Real functions (26-XX) 10 Group theory and generalizations (20-XX) 7 Topological groups, Lie groups (22-XX) 6 Associative rings and algebras (16-XX) 4 Order, lattices, ordered algebraic structures (06-XX) 4 Several complex variables and analytic spaces (32-XX) 3 Functions of a complex variable (30-XX) 3 Computer science (68-XX) 2 Ordinary differential equations (34-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX)

### Citations contained in zbMATH Open

96 Publications have been cited 2,050 times in 1,261 Documents Cited by Year
Tame topology and o-minimal structures. Zbl 0953.03045
van den Dries, Lou
1998
Geometric categories and o-minimal structures. Zbl 0889.03025
van den Dries, Lou; Miller, Chris
1996
$$p$$-adic and real subanalytic sets. Zbl 0693.14012
Denef, J.; van den Dries, Lou
1988
The elementary theory of restricted analytic fields with exponentiation. Zbl 0837.12006
van den Dries, Lou; Macintyre, Angus; Marker, David
1994
Gromov’s theorem on groups of polynomial growth and elementary logic. Zbl 0552.20017
van den Dries, Lou; Wilkie, A. J.
1984
A generalization of the Tarski-Seidenberg theorem, and some nondefinability results. Zbl 0612.03008
van den Dries, Lou
1986
On the real exponential field with restricted analytic functions. Zbl 0823.03017
van den Dries, Lou; Miller, Chris
1994
Dimension of definable sets, algebraic boundedness and Henselian fields. Zbl 0704.03017
van den Dries, Lou
1989
The real field with convergent generalized power series. Zbl 0905.03022
van den Dries, Lou; Speissegger, Patrick
1998
Bounds in the theory of polynomial rings over fields. A nonstandard approach. Zbl 0539.13011
van den Dries, Lou; Schmidt, K.
1984
Dense pairs of o-minimal structures. Zbl 0906.03036
van den Dries, Lou
1998
The field of reals with multisummable series and the exponential function. Zbl 1062.03029
van den Dries, Lou; Speissegger, Patrick
2000
Definable sets over finite fields. Zbl 0759.11045
Chatzidakis, Zoé; van den Dries, Lou; Macintyre, Angus
1992
The fields of real and complex numbers with a small multiplicative group. Zbl 1101.03028
van den Dries, Lou; Günaydin, Ayhan
2006
Elimination of quantifiers in algebraic structures. Zbl 0531.03016
Macintyre, Angus J.; McKenna, Kenneth; van den Dries, Lou
1983
Logarithmic-exponential power series. Zbl 0924.12007
van den Dries, Lou; Macintyre, Angus; Marker, David
1997
Subgroups of free profinite groups and large subfields of Q. Zbl 0485.20021
Lubotzky, Alexander; van den Dries, Lou
1981
Asymptotic differential algebra and model theory of transseries. Zbl 1430.12002
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2017
On the structure of semialgebraic sets over p-adic fields. Zbl 0692.14014
Scowcroft, Philip; van den Dries, Lou
1988
Algebraic theories with definable Skolem functions. Zbl 0596.03032
van den Dries, Lou
1984
Ultraproducts and approximation in local rings. I. Zbl 0416.13004
Becker, Joseph; Denef, J.; Lipshitz, L.; Van den Dries, Lou
1979
Logarithmic-exponential series. Zbl 0998.12014
van den Dries, Lou; Macintyre, Angus; Marker, David
2001
One-dimensional $$p$$-adic subanalytic sets. Zbl 0932.03038
van den Dries, Lou; Haskell, Deirdre; MacPherson, Dugald
1999
$$T$$-convexity and tame extensions. Zbl 0856.03028
van den Dries, Lou; Lewenberg, Adam H.
1995
The field of reals with a predicate for the powers of two. Zbl 0631.03020
van den Dries, Lou
1986
$$T$$-convexity and tame extensions. II. Zbl 0922.03055
van den Dries, Lou
1997
On the elementary theory of restricted elementary functions. Zbl 0698.03023
van den Dries, Lou
1988
Alfred Tarski’s elimination theory for real closed fields. Zbl 0651.03001
van den Dries, Lou
1988
Fields of surreal numbers and exponentiation. Zbl 0974.03035
van den Dries, Lou; Ehrlich, Philip
2001
Elimination theory for the ring of algebraic integers. Zbl 0659.12021
van den Dries, Lou
1988
Exponential rings, exponential polynomials and exponential functions. Zbl 0603.13019
van den Dries, Lou
1984
Remarks on Tarski’s problem concerning $$({\mathbb{R}},+,\cdot,\exp)$$. Zbl 0585.03006
van den Dries, Lou
1984
Decidability and undecidability theorems for PAC-fields. Zbl 0466.12017
Cherlin, Gregory; van den Dries, Lou; Macintyre, Angus J.
1981
An effective bound for groups of linear growth. Zbl 0567.20016
Wilkie, A. J.; van den Dries, Lou
1984
Some applications of a model theoretic fact to (semi-)algebraic geometry. Zbl 0538.14017
van den Dries, Lou
1982
o-minimal structures. Zbl 0861.03028
van den Dries, Lou
1996
Analytic Ax-Kochen-Ershov theorems. Zbl 0835.03004
van den Dries, Lou
1992
Quantifier elimination for linear formulas over ordered and valued fields. Zbl 0479.03018
Van den Dries, Lou
1981
O-minimal structures and real analytic geometry. Zbl 0980.03043
van den Dries, Lou
1999
Extending Tamm’s theorem. Zbl 0816.32004
van den Dries, Lou; Miller, Chris
1994
The logic of Rumely’s local-global principle. Zbl 0703.13021
van den Dries, Lou; Macintyre, Angus
1990
Closed asymptotic couples. Zbl 0974.12015
Aschenbrenner, Matthias; van den Dries, Lou
2000
$$H$$-fields and their Liouville extensions. Zbl 1066.12002
Aschenbrenner, Matthias; van den Dries, Lou
2002
o-minimal preparation theorems. Zbl 1081.03039
van den Dries, L.; Speissegger, P.
2002
Injective polynomial maps and the Jacobian conjecture. Zbl 0513.13007
Connell, E.; van den Dries, Lou
1983
Asymptotic differential algebra. Zbl 1087.12002
Aschenbrenner, Matthias; van den Dries, Lou
2005
A specialization theorem for analytic functions on compact sets. Zbl 0526.30004
van den Dries, Lou
1982
Classical model theory of fields. Zbl 0986.03034
van den Dries, Lou
2000
Artin-Schreier theory for commutative regular rings. Zbl 0376.13012
Van den Dries, Lou
1977
The absolute Galois group of a rational function field in characteristic zero is a semi-direct product. Zbl 0548.12013
van den Dries, Lou; Ribenboim, Paulo
1984
Liouville closed $$H$$-fields. Zbl 1134.12004
Aschenbrenner, Matthias; van den Dries, Lou
2005
Lectures on the model theory of valued fields. Zbl 1347.03074
van den Dries, Lou
2014
Generating the greatest common divisor, and limitations of primitive recursive algorithms. Zbl 1019.03027
van den Dries, L.
2003
Tarski’s problem and Pfaffian functions. Zbl 0616.03018
van den Dries, Lou
1986
Which curves over Z have points with coordinates in a discrete ordered ring? Zbl 0464.10047
van den Dries, Lou
1981
A specialization theorem for p-adic power series converging on the closed unit disc. Zbl 0511.12018
van den Dries, Lou
1981
Toward a model theory for transseries. Zbl 1314.03037
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2013
Elementary theory of valued fields with a valuation-preserving automorphism. Zbl 1235.03068
Azgin, Salih; van den Dries, Lou
2011
Mann pairs. Zbl 1192.03011
van den Dries, Lou; Günaydin, Ayhan
2010
Analytic Hardy fields and exponential curves in the real plane. Zbl 0597.26002
van den Dries, Lou
1984
Surjective polynomial maps, and a remark on the Jacobian problem. Zbl 0714.14013
McKenna, Ken; van den Dries, Lou
1990
Differentially algebraic gaps. Zbl 1151.12002
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2005
A linearly ordered ring whose theory admits elimination of quantifiers is a real closed field. Zbl 0397.06017
van den Dries, L. P. D.
1980
Weil’s group chunk theorem: A topological setting. Zbl 0764.22001
van den Dries, L. P. D.
1990
The surreal numbers as a universal $$H$$-field. Zbl 1470.12004
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2019
Images of additive polynomials in $$\mathbb{F}_q((t))$$ have the optimal approximation property. Zbl 1009.12008
van den Dries, Lou; Kuhlmann, Franz-Viktor
2002
A remark on Ax’s theorem on solvability modulo primes. Zbl 0744.11064
van den Dries, Lou
1991
Quantifier elimination for modules with scalar variables. Zbl 0772.03017
van den Dries, Lou; Holly, Jan
1992
New decidable fields of algebraic numbers. Zbl 0396.12020
van den Dries, Lou
1979
Application de la théorie des modeles aux groupes de Galois de corps de fonctions. Zbl 0426.12004
Van den Dries, Lou; Ribenboim, Paulo
1979
A Polish group without Lie sums. Zbl 1181.22006
van den Dries, Lou; Gao, Su
2009
A completeness theorem for trigonometric identities and various results on exponential functions. Zbl 0619.03012
van den Dries, Lou
1986
Is the Euclidean algorithm optimal among its peers? Zbl 1095.03025
van den Dries, Lou; Moschovakis, Yiannis N.
2004
Arithmetic complexity. Zbl 1367.68116
van den Dries, Lou; Moschovakis, Yiannis N.
2009
Globalizing locally compact local groups. Zbl 1203.22006
van den Dries, Lou; Goldbring, Isaac
2010
Isomorphism of complete local noetherian rings and strong approximation. Zbl 1154.13006
van den Dries, Lou
2008
Triangulation in o-minimal fields with standard part map. Zbl 1221.03030
van den Dries, Lou; Maříková, Jana
2010
Dimension in the realm of transseries. Zbl 1388.12008
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2017
On numbers, germs, and transseries. Zbl 1445.03044
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2018
On Skolem’s exponential functions below $$2^{2^ X}$$. Zbl 0556.03036
van den Dries, Lou; Levitz, Hilbert
1984
Correction to ”On the real exponential field with restricted analytic functions”. Zbl 0973.03514
van den Dries, Lou; Miller, Chris
1995
Erratum to “Globalizing locally compact local groups”. Zbl 1242.22005
van den Dries, Lou; Goldbring, Isaac
2012
Definable sets in Mann pairs. Zbl 1243.03054
van den Dries, Lou; Günaydin, Ayhan
2011
An application of Tarski’s principle to absolute Galois groups of function fields. Zbl 0645.12009
van den Dries, Lou; Ribenboim, Paulo
1987
An application of Tarski’s principle to absolute Galois groups of function fields. Zbl 0645.12010
van den Dries, Lou; Ribenboim, P.
1986
Some model theory and number theory for models of weak systems of arithmetic. Zbl 0454.03034
van den Dries, Lou
1980
Algorithms and bounds for polynomial rings. Zbl 0461.13015
van den Dries, Lou
1979
Elementary equivalence and the commutator subgroup. Zbl 0504.03006
van den Dries, L. P. D.; Glass, A. M. W.; Macintyre, Angus J.; Mekler, Alan H.; Poland, John
1982
Convergent series expansions of a new type for exponential functions. Zbl 0709.13011
van den Dries, Lou
1989
Locally compact contractive local groups. Zbl 1222.22004
van den Dries, Lou; Goldbring, Isaac
2009
The laws of integer divisibility, and solution sets of linear divisibility conditions. Zbl 1056.03020
van den Dries, L.; Wilkie, A. J.
2003
Invariant measures on groups satisfying various chain conditions. Zbl 1220.03024
van den Dries, Lou; Lopes, Vinicius Cifú
2011
On the elementary theory of rings of Witt vectors with a multiplicative set of representatives for the residue field. Zbl 0923.03053
van den Dries, Lou
1999
An intermediate value property for first-order differential polynomials. Zbl 0994.26005
van den Dries, Lou
2000
o-minimal structures on the field of real numbers. Zbl 0854.03036
van den Dries, Lou
1996
Maximal immediate extensions of valued differential fields. Zbl 1437.12003
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2018
The surreal numbers as a universal $$H$$-field. Zbl 1470.12004
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2019
On numbers, germs, and transseries. Zbl 1445.03044
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2018
Maximal immediate extensions of valued differential fields. Zbl 1437.12003
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2018
Asymptotic differential algebra and model theory of transseries. Zbl 1430.12002
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2017
Dimension in the realm of transseries. Zbl 1388.12008
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2017
Lectures on the model theory of valued fields. Zbl 1347.03074
van den Dries, Lou
2014
Toward a model theory for transseries. Zbl 1314.03037
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2013
Erratum to “Globalizing locally compact local groups”. Zbl 1242.22005
van den Dries, Lou; Goldbring, Isaac
2012
Elementary theory of valued fields with a valuation-preserving automorphism. Zbl 1235.03068
Azgin, Salih; van den Dries, Lou
2011
Definable sets in Mann pairs. Zbl 1243.03054
van den Dries, Lou; Günaydin, Ayhan
2011
Invariant measures on groups satisfying various chain conditions. Zbl 1220.03024
van den Dries, Lou; Lopes, Vinicius Cifú
2011
Mann pairs. Zbl 1192.03011
van den Dries, Lou; Günaydin, Ayhan
2010
Globalizing locally compact local groups. Zbl 1203.22006
van den Dries, Lou; Goldbring, Isaac
2010
Triangulation in o-minimal fields with standard part map. Zbl 1221.03030
van den Dries, Lou; Maříková, Jana
2010
A Polish group without Lie sums. Zbl 1181.22006
van den Dries, Lou; Gao, Su
2009
Arithmetic complexity. Zbl 1367.68116
van den Dries, Lou; Moschovakis, Yiannis N.
2009
Locally compact contractive local groups. Zbl 1222.22004
van den Dries, Lou; Goldbring, Isaac
2009
Isomorphism of complete local noetherian rings and strong approximation. Zbl 1154.13006
van den Dries, Lou
2008
The fields of real and complex numbers with a small multiplicative group. Zbl 1101.03028
van den Dries, Lou; Günaydin, Ayhan
2006
Asymptotic differential algebra. Zbl 1087.12002
Aschenbrenner, Matthias; van den Dries, Lou
2005
Liouville closed $$H$$-fields. Zbl 1134.12004
Aschenbrenner, Matthias; van den Dries, Lou
2005
Differentially algebraic gaps. Zbl 1151.12002
Aschenbrenner, Matthias; van den Dries, Lou; van der Hoeven, Joris
2005
Is the Euclidean algorithm optimal among its peers? Zbl 1095.03025
van den Dries, Lou; Moschovakis, Yiannis N.
2004
Generating the greatest common divisor, and limitations of primitive recursive algorithms. Zbl 1019.03027
van den Dries, L.
2003
The laws of integer divisibility, and solution sets of linear divisibility conditions. Zbl 1056.03020
van den Dries, L.; Wilkie, A. J.
2003
$$H$$-fields and their Liouville extensions. Zbl 1066.12002
Aschenbrenner, Matthias; van den Dries, Lou
2002
o-minimal preparation theorems. Zbl 1081.03039
van den Dries, L.; Speissegger, P.
2002
Images of additive polynomials in $$\mathbb{F}_q((t))$$ have the optimal approximation property. Zbl 1009.12008
van den Dries, Lou; Kuhlmann, Franz-Viktor
2002
Logarithmic-exponential series. Zbl 0998.12014
van den Dries, Lou; Macintyre, Angus; Marker, David
2001
Fields of surreal numbers and exponentiation. Zbl 0974.03035
van den Dries, Lou; Ehrlich, Philip
2001
The field of reals with multisummable series and the exponential function. Zbl 1062.03029
van den Dries, Lou; Speissegger, Patrick
2000
Closed asymptotic couples. Zbl 0974.12015
Aschenbrenner, Matthias; van den Dries, Lou
2000
Classical model theory of fields. Zbl 0986.03034
van den Dries, Lou
2000
An intermediate value property for first-order differential polynomials. Zbl 0994.26005
van den Dries, Lou
2000
One-dimensional $$p$$-adic subanalytic sets. Zbl 0932.03038
van den Dries, Lou; Haskell, Deirdre; MacPherson, Dugald
1999
O-minimal structures and real analytic geometry. Zbl 0980.03043
van den Dries, Lou
1999
On the elementary theory of rings of Witt vectors with a multiplicative set of representatives for the residue field. Zbl 0923.03053
van den Dries, Lou
1999
Tame topology and o-minimal structures. Zbl 0953.03045
van den Dries, Lou
1998
The real field with convergent generalized power series. Zbl 0905.03022
van den Dries, Lou; Speissegger, Patrick
1998
Dense pairs of o-minimal structures. Zbl 0906.03036
van den Dries, Lou
1998
Logarithmic-exponential power series. Zbl 0924.12007
van den Dries, Lou; Macintyre, Angus; Marker, David
1997
$$T$$-convexity and tame extensions. II. Zbl 0922.03055
van den Dries, Lou
1997
Geometric categories and o-minimal structures. Zbl 0889.03025
van den Dries, Lou; Miller, Chris
1996
o-minimal structures. Zbl 0861.03028
van den Dries, Lou
1996
o-minimal structures on the field of real numbers. Zbl 0854.03036
van den Dries, Lou
1996
$$T$$-convexity and tame extensions. Zbl 0856.03028
van den Dries, Lou; Lewenberg, Adam H.
1995
Correction to ”On the real exponential field with restricted analytic functions”. Zbl 0973.03514
van den Dries, Lou; Miller, Chris
1995
The elementary theory of restricted analytic fields with exponentiation. Zbl 0837.12006
van den Dries, Lou; Macintyre, Angus; Marker, David
1994
On the real exponential field with restricted analytic functions. Zbl 0823.03017
van den Dries, Lou; Miller, Chris
1994
Extending Tamm’s theorem. Zbl 0816.32004
van den Dries, Lou; Miller, Chris
1994
Definable sets over finite fields. Zbl 0759.11045
Chatzidakis, Zoé; van den Dries, Lou; Macintyre, Angus
1992
Analytic Ax-Kochen-Ershov theorems. Zbl 0835.03004
van den Dries, Lou
1992
Quantifier elimination for modules with scalar variables. Zbl 0772.03017
van den Dries, Lou; Holly, Jan
1992
A remark on Ax’s theorem on solvability modulo primes. Zbl 0744.11064
van den Dries, Lou
1991
The logic of Rumely’s local-global principle. Zbl 0703.13021
van den Dries, Lou; Macintyre, Angus
1990
Surjective polynomial maps, and a remark on the Jacobian problem. Zbl 0714.14013
McKenna, Ken; van den Dries, Lou
1990
Weil’s group chunk theorem: A topological setting. Zbl 0764.22001
van den Dries, L. P. D.
1990
Dimension of definable sets, algebraic boundedness and Henselian fields. Zbl 0704.03017
van den Dries, Lou
1989
Convergent series expansions of a new type for exponential functions. Zbl 0709.13011
van den Dries, Lou
1989
$$p$$-adic and real subanalytic sets. Zbl 0693.14012
Denef, J.; van den Dries, Lou
1988
On the structure of semialgebraic sets over p-adic fields. Zbl 0692.14014
Scowcroft, Philip; van den Dries, Lou
1988
On the elementary theory of restricted elementary functions. Zbl 0698.03023
van den Dries, Lou
1988
Alfred Tarski’s elimination theory for real closed fields. Zbl 0651.03001
van den Dries, Lou
1988
Elimination theory for the ring of algebraic integers. Zbl 0659.12021
van den Dries, Lou
1988
An application of Tarski’s principle to absolute Galois groups of function fields. Zbl 0645.12009
van den Dries, Lou; Ribenboim, Paulo
1987
A generalization of the Tarski-Seidenberg theorem, and some nondefinability results. Zbl 0612.03008
van den Dries, Lou
1986
The field of reals with a predicate for the powers of two. Zbl 0631.03020
van den Dries, Lou
1986
Tarski’s problem and Pfaffian functions. Zbl 0616.03018
van den Dries, Lou
1986
A completeness theorem for trigonometric identities and various results on exponential functions. Zbl 0619.03012
van den Dries, Lou
1986
An application of Tarski’s principle to absolute Galois groups of function fields. Zbl 0645.12010
van den Dries, Lou; Ribenboim, P.
1986
Gromov’s theorem on groups of polynomial growth and elementary logic. Zbl 0552.20017
van den Dries, Lou; Wilkie, A. J.
1984
Bounds in the theory of polynomial rings over fields. A nonstandard approach. Zbl 0539.13011
van den Dries, Lou; Schmidt, K.
1984
Algebraic theories with definable Skolem functions. Zbl 0596.03032
van den Dries, Lou
1984
Exponential rings, exponential polynomials and exponential functions. Zbl 0603.13019
van den Dries, Lou
1984
Remarks on Tarski’s problem concerning $$({\mathbb{R}},+,\cdot,\exp)$$. Zbl 0585.03006
van den Dries, Lou
1984
An effective bound for groups of linear growth. Zbl 0567.20016
Wilkie, A. J.; van den Dries, Lou
1984
The absolute Galois group of a rational function field in characteristic zero is a semi-direct product. Zbl 0548.12013
van den Dries, Lou; Ribenboim, Paulo
1984
Analytic Hardy fields and exponential curves in the real plane. Zbl 0597.26002
van den Dries, Lou
1984
On Skolem’s exponential functions below $$2^{2^ X}$$. Zbl 0556.03036
van den Dries, Lou; Levitz, Hilbert
1984
Elimination of quantifiers in algebraic structures. Zbl 0531.03016
Macintyre, Angus J.; McKenna, Kenneth; van den Dries, Lou
1983
Injective polynomial maps and the Jacobian conjecture. Zbl 0513.13007
Connell, E.; van den Dries, Lou
1983
Some applications of a model theoretic fact to (semi-)algebraic geometry. Zbl 0538.14017
van den Dries, Lou
1982
A specialization theorem for analytic functions on compact sets. Zbl 0526.30004
van den Dries, Lou
1982
Elementary equivalence and the commutator subgroup. Zbl 0504.03006
van den Dries, L. P. D.; Glass, A. M. W.; Macintyre, Angus J.; Mekler, Alan H.; Poland, John
1982
Subgroups of free profinite groups and large subfields of Q. Zbl 0485.20021
Lubotzky, Alexander; van den Dries, Lou
1981
Decidability and undecidability theorems for PAC-fields. Zbl 0466.12017
Cherlin, Gregory; van den Dries, Lou; Macintyre, Angus J.
1981
Quantifier elimination for linear formulas over ordered and valued fields. Zbl 0479.03018
Van den Dries, Lou
1981
Which curves over Z have points with coordinates in a discrete ordered ring? Zbl 0464.10047
van den Dries, Lou
1981
A specialization theorem for p-adic power series converging on the closed unit disc. Zbl 0511.12018
van den Dries, Lou
1981
A linearly ordered ring whose theory admits elimination of quantifiers is a real closed field. Zbl 0397.06017
van den Dries, L. P. D.
1980
Some model theory and number theory for models of weak systems of arithmetic. Zbl 0454.03034
van den Dries, Lou
1980
Ultraproducts and approximation in local rings. I. Zbl 0416.13004
Becker, Joseph; Denef, J.; Lipshitz, L.; Van den Dries, Lou
1979
New decidable fields of algebraic numbers. Zbl 0396.12020
van den Dries, Lou
1979
Application de la théorie des modeles aux groupes de Galois de corps de fonctions. Zbl 0426.12004
Van den Dries, Lou; Ribenboim, Paulo
1979
Algorithms and bounds for polynomial rings. Zbl 0461.13015
van den Dries, Lou
1979
Artin-Schreier theory for commutative regular rings. Zbl 0376.13012
Van den Dries, Lou
1977
all top 5

### Cited by 984 Authors

 33 van den Dries, Lou 26 Cluckers, Raf 22 Miller, Chris 22 Peterzil, Ya’acov 20 Edmundo, Mário J. 18 Pillay, Anand 17 Starchenko, Sergei 16 Aschenbrenner, Matthias 16 Eleftheriou, Pantelis E. 16 Kaiser, Tobias 16 Rolin, Jean-Philippe 15 Fischer, Andreas M. 15 Phạm Tiên So’n 15 Point, Françoise 14 Hieronymi, Philipp 14 Macintyre, Angus John 14 Speissegger, Patrick 13 Macpherson, Dugald 13 Pila, Jonathan 12 Hrushovski, Ehud 12 Schoutens, Hans 10 Bolte, Jérôme 10 Halupczok, Immanuel 10 Kuhlmann, Salma 10 Lewis, Adrian S. 10 Lion, Jean-Marie 10 Pierzchała, Rafał 10 Valette, Guillaume 9 Berenstein, Alexander 9 Drusvyatskiy, Dmitriy 9 Haskell, Deirdre 9 Hasson, Assaf 9 Prelli, Luca 9 Steinhorn, Charles I. 8 Berarducci, Alessandro 8 Fornasiero, Antongiulio 8 Jarden, Moshe 8 Le Gal, Olivier 8 Lubotzky, Alexander 8 Matusinski, Mickaël 8 Onshuus, Alf Angel 8 Servi, Tamara 8 Tressl, Marcus 8 Vassiliev, Evgueni V. 8 Walsberg, Erik 8 Wilkie, Alex James 7 Bélair, Luc 7 Fujita, Masato 7 Gaubert, Stéphane 7 Günaydın, Ayhan 7 Ioffe, Alexander Davidovich 7 Kuhlmann, Franz-Viktor 7 Loeser, François 7 Mamino, Marcello 7 Marker, David E. 7 van der Hoeven, Joris 6 Basu, Saugata 6 Bianconi, Ricardo 6 Bowditch, Brian H. 6 Chatzidakis, Zoé Maria 6 Daniilidis, Aris 6 Denef, Jan 6 Gehret, Allen 6 Guzy, Nicolas 6 Haran, Dan 6 Kaplan, Elliot 6 Kurdyka, Krzysztof 6 Leenknegt, Eva 6 León Sánchez, Omar 6 Lipshitz, Leonard 6 Maříková, Jana 6 Sanz Sánchez, Fernando 6 Sapir, Mark Valentinovich 6 Scowcroft, Philip 6 Shiota, Masahiro 6 Terzo, Giuseppina 6 Thamrongthanyalak, Athipat 6 Tsimerman, Jacob 6 Wu, Chunlin 5 Baro, Elías 5 Bernig, Andreas 5 Binyamini, Gal 5 Chernikov, Artem 5 Comte, Georges 5 Cubides Kovacsics, Pablo 5 du Sautoy, Marcus P. F. 5 Ehrlich, Philip 5 Fichou, Goulwen 5 Gabrielov, Andrei 5 Hoffmann, Daniel Max 5 Laskowski, Michael Chris 5 Loi, Ta Le 5 Michaux, Christian 5 Nguyêñ Duy Tân 5 Novikov, Dmitry 5 Otero, Margarita 5 Pawłucki, Wiesław 5 Popescu, Dorin 5 Tari, Somayyeh 5 Tent, Katrin ...and 884 more Authors
all top 5

### Cited in 218 Serials

 108 The Journal of Symbolic Logic 86 Annals of Pure and Applied Logic 57 Journal of Algebra 47 Proceedings of the American Mathematical Society 44 Transactions of the American Mathematical Society 41 Israel Journal of Mathematics 35 Archive for Mathematical Logic 34 Journal of Pure and Applied Algebra 31 Advances in Mathematics 26 Annales de l’Institut Fourier 21 Mathematical Logic Quarterly (MLQ) 20 The Bulletin of Symbolic Logic 18 Journal of Symbolic Computation 17 Manuscripta Mathematica 17 Notre Dame Journal of Formal Logic 17 Selecta Mathematica. New Series 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 16 Duke Mathematical Journal 16 Journal of Mathematical Logic 15 Mathematische Annalen 14 Communications in Algebra 13 Inventiones Mathematicae 13 Theoretical Computer Science 13 Bulletin of the American Mathematical Society. New Series 12 Compositio Mathematica 12 Mathematical Programming. Series A. Series B 11 Journal für die Reine und Angewandte Mathematik 11 Mathematische Zeitschrift 11 SIAM Journal on Optimization 11 Journal of the Institute of Mathematics of Jussieu 10 Journal of Mathematical Analysis and Applications 10 Illinois Journal of Mathematics 10 Journal of the American Mathematical Society 9 Journal of Optimization Theory and Applications 9 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 9 Annals of Mathematics. Second Series 9 Journal of the European Mathematical Society (JEMS) 8 Archiv der Mathematik 8 Geometriae Dedicata 8 International Journal of Algebra and Computation 7 Discrete & Computational Geometry 6 Geometry & Topology 6 Advances in Geometry 6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 5 Fundamenta Mathematicae 5 Journal of Computer and System Sciences 5 Journal of Differential Equations 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Bulletin of the London Mathematical Society 4 Publications Mathématiques 4 Mathematics of Operations Research 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Proceedings of the London Mathematical Society. Third Series 4 Topology and its Applications 4 Journal of Complexity 4 The Journal of Geometric Analysis 4 Geometric and Functional Analysis. GAFA 4 Journal de Mathématiques Pures et Appliquées. Neuvième Série 4 Theory of Computing Systems 4 Set-Valued and Variational Analysis 3 Journal d’Analyse Mathématique 3 Algebra and Logic 3 Annales Polonici Mathematici 3 Journal of Mathematical Economics 3 Nagoya Mathematical Journal 3 Linear Algebra and its Applications 3 Journal of Mathematical Imaging and Vision 3 Revista Matemática Complutense 3 RAIRO. Theoretical Informatics and Applications 3 Algebraic & Geometric Topology 3 Foundations of Computational Mathematics 3 Central European Journal of Mathematics 3 Journal of Algebra and its Applications 3 Groups, Geometry, and Dynamics 3 Journal of Logic and Analysis 3 Forum of Mathematics, Sigma 2 Discrete Mathematics 2 Inverse Problems 2 Mathematical Notes 2 Acta Mathematica 2 Acta Mathematica Vietnamica 2 Canadian Mathematical Bulletin 2 Commentarii Mathematici Helvetici 2 Journal of Functional Analysis 2 Journal of the London Mathematical Society. Second Series 2 Journal of the Mathematical Society of Japan 2 Journal of Number Theory 2 Mathematische Nachrichten 2 Mathematika 2 Memoirs of the American Mathematical Society 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Pacific Journal of Mathematics 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Rendiconti del Seminario Matematico della Università di Padova 2 Revista Matemática Iberoamericana 2 Japan Journal of Industrial and Applied Mathematics 2 Differential Geometry and its Applications 2 IMRN. International Mathematics Research Notices 2 L’Enseignement Mathématique. 2e Série ...and 118 more Serials
all top 5

### Cited in 53 Fields

 725 Mathematical logic and foundations (03-XX) 310 Algebraic geometry (14-XX) 298 Field theory and polynomials (12-XX) 159 Several complex variables and analytic spaces (32-XX) 155 Number theory (11-XX) 146 Group theory and generalizations (20-XX) 110 Commutative algebra (13-XX) 83 Computer science (68-XX) 69 Real functions (26-XX) 63 Order, lattices, ordered algebraic structures (06-XX) 56 Calculus of variations and optimal control; optimization (49-XX) 52 Operations research, mathematical programming (90-XX) 45 Manifolds and cell complexes (57-XX) 44 Topological groups, Lie groups (22-XX) 44 Differential geometry (53-XX) 44 Global analysis, analysis on manifolds (58-XX) 34 Combinatorics (05-XX) 33 General topology (54-XX) 30 Ordinary differential equations (34-XX) 30 Dynamical systems and ergodic theory (37-XX) 30 Numerical analysis (65-XX) 29 Associative rings and algebras (16-XX) 22 Functions of a complex variable (30-XX) 22 Algebraic topology (55-XX) 17 Functional analysis (46-XX) 14 Convex and discrete geometry (52-XX) 13 General and overarching topics; collections (00-XX) 12 Measure and integration (28-XX) 11 Category theory; homological algebra (18-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 10 Geometry (51-XX) 9 Linear and multilinear algebra; matrix theory (15-XX) 9 Approximations and expansions (41-XX) 9 Probability theory and stochastic processes (60-XX) 8 History and biography (01-XX) 8 Partial differential equations (35-XX) 8 Operator theory (47-XX) 8 Information and communication theory, circuits (94-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 6 Statistics (62-XX) 5 General algebraic systems (08-XX) 5 Special functions (33-XX) 5 Systems theory; control (93-XX) 4 $$K$$-theory (19-XX) 4 Potential theory (31-XX) 4 Difference and functional equations (39-XX) 3 Abstract harmonic analysis (43-XX) 2 Nonassociative rings and algebras (17-XX) 2 Integral transforms, operational calculus (44-XX) 2 Mechanics of particles and systems (70-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Sequences, series, summability (40-XX)

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