Anand Pillay

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Anand Pillay is affiliated with the following schools: University of Oxford, University of Notre Dame, University of Illinois Urbana-Champaign, University of Manchester

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Anand Pillay

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Anand Pillay's Degrees

PhD Mathematics University of Manchester

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According to Wikipedia, Anand Pillay is a British mathematician and logician working in model theory and its applications in algebra and number theory. Biography Pillay studied as an undergraduate at the University of Oxford, obtaining a Bachelor in Mathematics and Philosophy in 1973 at Balliol College. At the University of London, he received his master's degree in mathematics in 1974 and his PhD in 1978 with Wilfrid Hodges at Bedford College, titled Gaifman Operations, Minimal Models, and the Number of Countable Models. In 1978, he was a Royal Society Fellow and visiting scientist at CNRS at Paris Diderot University. After teaching at the University of Manchester starting in 1981 and at McGill University in Canada, he joined the University of Notre Dame as an assistant professor in 1983, where he became an associate professor in 1986 and a full professor in 1988. From 1996 to 2006, he was Swanlund Professor at the University of Illinois Urbana-Champaign, where he is now Professor Emeritus. Since 2005, he has been the Chair of Mathematical Logic at the University of Leeds. He also held positions as a visiting scholar at the Fields Institute in Toronto, at the Mathematical Sciences Research Institute in Berkeley, and at the Isaac Newton Institute in Cambridge.

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Anand Pillay's Published Works

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Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Geometric Stability Theory (1996) (433)
Simple Theories (1997) (324)
Model theory with applications to algebra and analysis (2008) (319)
DEFINABLE SETS IN ORDERED STRUCTURES. I (1986) (294)
Definable sets in ordered structures (1984) (287)
Introduction to stability theory (1983) (257)
Models of Peano Arithmetic (1981) (248)
Groups, measures, and the NIP (2006) (215)
On groups and fields definable in o-minimal structures (1988) (201)
On NIP and invariant measures (2007) (189)
Generic Structures and Simple Theories (1998) (152)
Groups definable in local fields and pseudo-finite fields (1994) (142)
Model theory of fields (2017) (130)
Weakly normal groups (1985) (116)
Coordinatisation and canonical bases in simple theories (2000) (103)
Jet spaces of varieties over differential and difference fields (2003) (88)
Definably simple groups in o-minimal structures (2000) (82)
Type-Definability, Compact Lie Groups, and O-Minimality (2004) (76)
Lovely pairs of models (2003) (69)
DEFINABLE SETS IN ORDERED STRUCTURES. II (2010) (65)
First order topological structures and theories (1987) (65)
Galois Groups of First order Theories (2001) (63)
Hyperimaginaries and automorphism groups (2001) (62)
A Note on the Axioms for Differentially Closed Fields of Characteristic Zero (1998) (62)
A Note on the Axioms for Differentially Closed Fields of Characteristic Zero (1998) (62)
A descending chain condition for groups definable in o-minimal structures (2005) (55)
Linear Groups Definable in o-Minimal Structures☆ (2002) (55)
Some foundational questions concerning differential algebraic groups (1997) (55)
Definable subgroups of algebraic groups over finite fields. (1995) (54)
On Groups and Rings Definable In O–Minimal Expansions of Real Closed Fields (1996) (52)
Forking in the category of existentially closed structures (2000) (51)
Generic sets in definably compact groups (2007) (46)
On central extensions and definably compact groups in o-minimal structures (2008) (46)
Generically stable and smooth measures in NIP theories (2010) (44)
Connected components of definable groups, and o-minimality II (2011) (43)
The geometry of forking and groups of finite Morley rank (1995) (43)
Simple algebraic and semialge-braic groups over real-closed elds (2000) (42)
Definability and definable groups in simple theories (1998) (41)
The Prospects for Mathematical Logic in the Twenty-First Century (2001) (41)
Additive reducts of real closed fields (1992) (40)
A note on CM-triviality and the geometry of forking (2000) (40)
Model theory of algebraically closed fields (1998) (37)
On algebraic relations between solutions of a generic Painleve equation (2011) (36)
Algebraic D-groups and differential Galois theory (2004) (36)
Countable models of stable theories (1983) (36)
Generic stability, regularity, and quasi-minimality (2009) (36)
Some remarks on definable equivalence relations in O-minimal structures (1986) (35)
Definable groups and compact p‐adic Lie groups (2008) (35)
A Lindemann-Weierstrass theorem for semi-abelian varieties over function fields (2008) (35)
Closed sets and chain conditions in stable theories (1984) (35)
Relative Manin–Mumford for Semi-Abelian Surfaces (2013) (34)
Differential Algebraic Groups and the Number of Countable Differentially Closed Fields (2005) (33)
Between Groups and rings (1989) (32)
Primitive Permutation Groups of Finite Morley Rank (1995) (32)
Discrete o-minimal structures (1987) (31)
Quantifier elimination for algebraic $D$-groups (2005) (31)
From Stability to Simplicity (1998) (31)
Dimension theory and homogeneity for elementary extensions of a model (1982) (30)
On algebraic $\sigma$-groups (2006) (30)
On Theories Having Three Countable Models (1998) (30)
Superrosy dependent groups having finitely satisfiable generics (2007) (29)
On canonical bases and internality criteria (2007) (29)
Models, Logics, and Higher-dimensional Categories: A Tribute to the Work of Mihaly Makkai (2011) (29)
A note on groups definable in difference fields (2001) (29)
Effective bounds for the number of transcendental points on subvarieties of semi-abelian varieties (2000) (29)
A group version of stable regularity (2017) (28)
An application of model theory to real and p-adic algebraic groups (1989) (28)
On genericity and weight in the free group (2008) (28)
Some model theory of compact complex spaces (2000) (28)
On compactifications and the topological dynamics of definable groups (2012) (27)
Model-theoretic consequences of a theorem of Campana and Fujiki (2002) (27)
Definability of types, and pairs of O-minimal structures (1994) (27)
Introduction to the Model Theory of Fields (1996) (26)
FORKING IN THE FREE GROUP (2007) (26)
A survey of asymptotic classes and measurable structures (2008) (25)
Sheaves of continuous definable functions (1988) (24)
Differential Galois theory I (1998) (24)
Model theory and diophantine geometry (1997) (23)
The definable multiplicity property and generic automorphisms (2000) (23)
The model-theoretic content of Lang’s conjecture (1998) (22)
Model theory, algebra, and geometry (2000) (22)
External definability and groups in NIP theories (2013) (22)
On the algebraic independence of generic Painlevé transcendents (2012) (22)
Affine Nash groups over real closed fields (2011) (22)
Generalised Bohr compactification and model-theoretic connected components (2014) (21)
Differential arcs and regular types in differential fields (2008) (21)
Topological dynamics and the complexity of strong types (2015) (20)
Some model theory of compact Lie groups (1991) (20)
Classification theory over a predicate. I (1985) (20)
Model Theory of Fields: Lecture Notes in Logic 5, Second Edition (2005) (20)
Cohomology of Structures and Some Problems of Ahlbrandt and Ziegler (1994) (20)
Differential Galois theory III: Some inverse problems (1997) (20)
Topological dynamics and definable groups (2012) (19)
Meromorphic Groups (2000) (19)
Some model theory of SL(2,R) (2012) (19)
Bodies and surgery (1995) (19)
Around stable forking (2001) (19)
Stable Theories, Pseudoplanes and the Number of Countable Models (1989) (18)
Forking and Pushouts in Modules (1983) (18)
Reducts of (C, +, ·) which contain + (1990) (18)
Model Theory, Differential Algebra, and Number Theory (1995) (18)
A group in a group (1990) (17)
On PAC and bounded substructures of a stable structure (2006) (17)
Schanuel's conjecture for non-isoconstant elliptic curves over function fields (2008) (17)
On Lascar rank and Morley rank of definable groups in differentially closed fields (2002) (16)
The Model theory of groups (1989) (16)
On groups and fields interpretable in torsion-free hyperbolic groups (2012) (16)
Some model theory of separably closed fields (1996) (16)
Structure and regularity for subsets of groups with finite VC-dimension (2018) (16)
Pro-algebraic and differential algebraic group structures on affine spaces (2000) (16)
Groups of Dimension Two and Three Over o-Minimal Structures (1991) (16)
Some observations about the real and imaginary parts of complex Pfaffian functions (2008) (15)
Compact complex manifolds with the DOP and other properties (2002) (15)
Forking, normalization and canonical bases (1986) (15)
SOME DEFINABLE GALOIS THEORY AND EXAMPLES (2015) (15)
Remarks on the NIP in a model (2017) (15)
Some model theory and topological dynamics of $p$-adic algebraic groups (2017) (14)
UNIVERSAL COVERS OF COMMUTATIVE FINITE MORLEY RANK GROUPS (2014) (14)
On minimal flows. definably amenable groups, and o-minimality (2015) (14)
Borel Equivalence Relations and Lascar Strong Types (2012) (13)
Remarks on Galois cohomology and definability (1997) (13)
Interpretations and differential Galois extensions (2014) (13)
On countable simple unidimensional theories (2003) (13)
Remarks on Tao's algebraic regularity lemma (2013) (13)
Modules and stability theory (1987) (13)
Computing all identifiable functions of parameters for ODE models (2020) (13)
Differential Galois Theory II (1997) (13)
On the canonical base property (2012) (12)
Amenability, definable groups, and automorphism groups (2016) (12)
Two remarks on differential fields (2002) (12)
Some model theory of fibrations and algebraic reductions (2012) (12)
Elliptic and Hyperelliptic Curves Over Supersimple Fields (2004) (11)
Remarks on algebraic D-varieties and the model theory of differential fields (2016) (11)
Stable theories without dense forking chains (1992) (11)
On externally definable sets and a theorem of Shelah (2006) (11)
Mordell–Lang conjecture for function fields in characteristic zero, revisited (2004) (11)
On Levi subgroups and the Levi decomposition for groups definable in o-minimal structures (2011) (10)
On fields definable inQp (1989) (10)
GENERIC STABILITY AND STABILITY (2012) (10)
Canonical bases in o-minimal and related structures (2006) (10)
Multi-experiment parameter identifiability of ODEs and model theory (2020) (10)
Supersimple fields and division rings (1998) (10)
On stable fields and weight (2009) (10)
ℵ0-categoricity over a predicate (1983) (10)
Stable embeddedness and NIP (2010) (10)
Model Theory in Algebra, Analysis and Arithmetic (2014) (10)
Remarks on compactifications of pseudofinite groups (2015) (9)
Finite-dimensional differential algebraic groups and the Picard-Vessiot theory (2002) (9)
Classifi cation over a predicate II (1985) (9)
The stable regularity lemma revisited (2015) (9)
Superstable differential fields (1992) (9)
Notes on model companions of stable theories with an automorphism (2001) (9)
Imaginaries in pairs of algebraically closed fields (2007) (9)
SEMIABELIAN VARIETIES OVER SEPARABLY CLOSED FIELDS, MAXIMAL DIVISIBLE SUBGROUPS, AND EXACT SEQUENCES (2009) (9)
Amenability, connected components, and definable actions (2019) (9)
Instability and theories with few models (1980) (9)
Differentially algebraic group chunks (1990) (9)
Imaginaries in beautiful pairs (2004) (8)
Number of countable models (1978) (8)
Countable models of 1-based theories (1992) (8)
Semisimple Stable and Superstable Groups (1989) (8)
On first order amenability (2020) (8)
Remarks on a theorem of Campana and Fujiki (2001) (8)
SATURATED FREE ALGEBRAS REVISITED (2014) (8)
A note on groups definable in the p-adic field (2018) (8)
Strongly minimal pseudofinite structures (2014) (7)
On function field Mordell-Lang and Manin-Mumford (2014) (7)
Computing all identifiable functions for ODE models (2020) (7)
On the topological dynamics of automorphism groups: a model-theoretic perspective (2019) (7)
Non-totally transcendental unidimensional theories (1990) (7)
Model Theory with Applications to Algebra and Analysis: Model theory and stability theory, with applications in differential algebra and algebraic geometry (2008) (7)
Model Theory, Stability Theory, and Stable Groups (1989) (7)
A Note on Generically Stable Measures and fsg Groups (2011) (7)
Pseudofinite groups and VC-dimension (2018) (7)
Embedded Picard–Vessiot extensions (2017) (6)
Theories with exactly three countable models and theories with algebraic prime models (1980) (6)
A note on finitely generated models (1983) (6)
On the isotriviality of projective iterative ∂-varieties (2012) (6)
Forking and fundamental order in simple theories (1999) (6)
GROUP COVERS, o-MINIMALITY, AND CATEGORICITY (2010) (6)
Superstable theories with few countable models (1992) (6)
Remarks on unimodularity (2010) (6)
Simple groups definable in O-minimal structures (1998) (6)
The Picard-Vessiot theory, constrained cohomology, and linear differential algebraic groups (2016) (6)
Definable $f$-Generic Groups over $p$-Adic Numbers (2019) (5)
Weakly homogeneous models (1982) (5)
Galois theory, functional Lindemann-Weierstrass, and Manin maps. (2015) (5)
DOMINATION AND REGULARITY (2018) (5)
Simple superstable theories (1987) (5)
Superstable groups of finite rank without pseudoplanes (1986) (5)
ACFA and the Manin-Mumford Conjecture (1997) (5)
A remark on differential algebraic groups. (1992) (4)
Definable Sets in Generic Complex Tori (1996) (4)
Some remarks on nonmultidimensional superstable theories (1994) (4)
Corrigendum to: “On Lascar rank and Morley rank of definable groups in differentially closed fields” (2009) (4)
Some remarks on modular regular types (1991) (4)
Differential Galois cohomology and parameterized Picard–Vessiot extensions (2019) (4)
ℵ_{0}-categorical strongly minimal compact complex manifolds (2012) (4)
Triviality, NDOP and Stable Varieties (1993) (4)
Definability and elementary equivalence in the Ershov difference hierarchy (2009) (4)
Tiny models of categorical theories (1992) (4)
A GAP THEOREM FOR ABELIAN VARIETIES OVER DIFFERENTIAL FIELDS (1997) (4)
Generalized Picard–Vessiot extensions and differential Galois cohomology (2017) (4)
Stable groups and expansions of $(\mathbb{Z},+,0)$ (2016) (4)
Gaifman operations, minimal models and the number of countable models (1977) (4)
Mordell-Lang for function elds in characteristic zero, revisited (2004) (4)
A note on subgroups of the automorphism group of a saturated model, and regular types (1989) (3)
On Lovely Pairs and the (∃ y ∈ P) Quantifier (2005) (3)
ON MAXIMAL STABLE QUOTIENTS OF DEFINABLE GROUPS IN NIP THEORIES (2016) (3)
Embeddings into the Turing degrees (2009) (3)
On the number of models of uncountable theories (1994) (3)
INDEXED LAWVERE THEORIES for LOCAL STATE (2010) (3)
Minimal types in simple theories (2006) (3)
Relative internality and definable fibrations (2020) (3)
On Dedekind complete o-minimal structures (1987) (3)
Amalgamations preserving ℵ1-categoricity (1997) (3)
On pp-elimination and stability in a continuous setting (2021) (3)
Partition properties and definable types in Peano Arithmetic (1981) (2)
Model Theory with Applications to Algebra and Analysis: Model theory and Kähler geometry (2008) (2)
Uncountable categoricity for gross models (2004) (2)
Morley ’ s theorem for gross models (2002) (2)
On definable Galois groups and the strong canonical base property (2016) (2)
INVARIANT MEASURES IN SIMPLE AND IN SMALL THEORIES (2021) (2)
Cuts in Models of Arithmetic (1981) (2)
Strong dependence, weight, and measure (2010) (2)
Model theory and Kaehler geometry (2007) (2)
Number of models of theories with many types (1979) (2)
A note on nonmultidimensional superstable theories (1985) (2)
The free group has the dimensional order property (2016) (2)
Erratum to “Model Theory and Diophantine Geometry” (1998) (2)
A note on tight stable theorie (1983) (2)
Open Subgroups of GL 2 (Q p ). (1989) (2)
Regular types in nonmultidimensional ω-stable theories (1984) (2)
Open Subgroups of GL2(Qp) (1989) (2)
Unidimensional Modules: Uniqueness of Maximal Non-Modular Submodels (1993) (1)
Stability Theoretic Methods in Unstable Theories (2009) (1)
Strongly minimal pseudonite structures (2014) (1)
Pseudofinite Model Theory (2015) (1)
Aspects of Geometric Model Theory (2001) (1)
SUPERSTRONG IS STRONG ENOUGH (1998) (1)
Book Review: Uncountably categorical theories (1994) (1)
Weight and Measure in NIP Theories (2013) (1)
On function field Mordell–Lang: the semiabelian case and the socle theorem (2017) (1)
Applications of logic in algebra: Examples from clone theory (2009) (1)
Model Theory with Applications to Algebra and Analysis: Differential algebra and generalizations of Grothendieck's conjecture on the arithmetic of linear differential equations (2008) (1)
On a question of Herzog and Rothmaler (2004) (1)
Subvarieties of commutative meromorphic groups (2004) (1)
Book Review: Zariski geometries. Geometry from the logician’s point of view (2012) (1)
Weakly definable types (1986) (1)
On the Manin-Mumford conjecture (2003) (1)
Model Theory with Applications to Algebra and Analysis: Volume 1 (2008) (1)
Model Theory: Around Valued Fields and Dependent Theories (2010) (1)
Almost Indiscernible Theories and Saturated Free Algebras (2019) (1)
A note on existentially closed difference fields with algebraically closed fixed field (2001) (1)
On types of CB-rank 1 in simple theories (2008) (1)
Remarks on theories of free algebras and modules (2020) (1)
Lecture notes on strongly minimal sets ( and fields ) with a generic automorphism (1999) (1)
Some results on permutation group isomorphism and categoricity (2002) (1)
Connected components of groups and o-minimal expansions of real closed fields (2013) (1)
A guide to classical and modern model theory(Trends in Logic — Studia Logica Library 19)By Annalisa Marcja and Carlo Toffalori: 369 pp.,£77.00 (US$115.00, 120.00 euro), isbn 1-4020-1330-2(Kluwer Academic Publishers, Dordrecht, 2003) (2007) (1)
Groups , measures , and the NIP Ehud Hrushovski (2008) (1)
On groups with definable $f$-generics definable in $p$-adically closed fields (2019) (1)
Saturated free algebras and almost indiscernible theories (2019) (1)
A note on groups definable in the p-adic field (2019) (0)
Some model theory of fibrations and algebraic reductions (2014) (0)
Hrushovski Ehud and Zilber Boris. Zariski geometries, Journal of the American Mathematical Society, vol. 9 (1996), pp. 1–56. (1999) (0)
On stable elds and weight (2010) (0)
More on Galois cohomology, definability and differential algebraic groups (2021) (0)
Groups definable in o-minimal structures: structure theorem, G^000, definable amenability and bounded orbits (2010) (0)
Review: John T. Baldwin, Fundamentals of Stability Theory (1992) (0)
Preface (Special issue on Logic Colloquium 2006) (2008) (0)
Review: Wilfrid Hodges, Model Theory (1995) (0)
K 0 -categoricity in Regular Subsets of L (c0\(o (2006) (0)
MODEL THEORY , STABILITY THEORY & STABLE GROUPS (0)
Model theory in algebra, analysis and arithmetic : Cetraro, Italy 2012 (2014) (0)
Lecture notes- Applied Stability Theory (Math 414) Autumn 2003. (2003) (0)
ℵ0‐Categoricity in Regular Subsets of Lω1ω (1980) (0)
Approximate subgroups with bounded VC-dimension (2020) (0)
Stability and Grothendieck (2017) (0)
1 Model theory and groups (2021) (0)
A note on Pontryagin duality and continuous logic (2022) (0)
Interactions between model theory and geometry (2004) (0)
Model theory of proalgebraic groups (2019) (0)
2 Difference fields and differential fields (2003) (0)
Interpretations and differential Galois extensions . DRAFT (2014) (0)
$\aleph_0$-categorical strongly minimal compact complex manifolds (2010) (0)
A MODEL-THEORETIC PERSPECTIVE ON ALGEBRAIC REDUCTIONS OF HYPERKAEHLER MANIFOLDS (2012) (0)
Model Theory and Groups (2021) (0)
Arithmetic Geometry ( 5 th January 1998-3 rd June 1998 ) (2014) (0)
Generalized Picard-Vessiot extensions and differential (2017) (0)
Remarks on Purity of Methods (2021) (0)
Book Review: A course in model theory: An introduction to contemporary mathematical logic (2001) (0)
Well-definable types over subsets (1982) (0)
Model Theory , Algebra , and Geometry MSRI Publications Volume 39 , 2000 Overview (2001) (0)
A Class of ℵ0-Categorical Theories (1981) (0)
Some Themes Around First Order Theories Without the Independence Property (2014) (0)
Model Theory with Applications to Algebra and Analysis: Preface (2008) (0)
Aspects of geometricmodel theory (2016) (0)
Tighter Bounds on the Expressivity of Transformer Encoders (2023) (0)
A remark on multivalued algebraic groups (2008) (0)
On the canonical base property (2013) (0)
A pr 2 01 2 Borel equivalence relations and Lascar strong types (2013) (0)
DOSEN, K., Rudimentary Kripke models for the intuitionistic propositional calculus EVANS, DM and HRUSHOVSKI, E., On the automorphism groups of finite covers (1993) (0)
Amalgamations Preserving aleph0-Categoricity (1997) (0)
Topics in Stability Theory (2019) (0)
Algebraic Theory of Differential Equations: Around Differential Galois Theory (2008) (0)
A note on the effective listing of complete types (2019) (0)
Some Foundational Questions concerning Differential Algebraic Groups Anand Pillay (1997) (0)
Ju l 2 01 8 A note on groups definable in the p-adic field (2018) (0)
Open subgroups of $p$-adic algebraic groups (2023) (0)
Ju n 20 18 Domination and regularity (2018) (0)
INTRODUCTION TO GEOMETRIC STABILITY (2017) (0)
Thorn forking, weak normality, and theories with selectors (2020) (0)
Notre Dame, Indiana May 20–May 23, 2009 (2009) (0)
Lecture notes - Stability Theory (Math 414) (2003) (0)
L O ] 8 S ep 2 02 1 Model theory and groups (2021) (0)
AN ENGLISH TRANSLATION OF CORPS ET CHIRURGIE ( FIELDS AND SURGERY (2016) (0)
Logic Colloquium 2006: Introduction (2009) (0)
PRIMITIVE PERMUTATION GROUPS OF FINITE MORLEY RANK DUGALD MACPHERSON and ANAND PILLAY (1995) (0)
On minimal ﬂows, deﬁnably amenable groups, and o -minimality (2015) (0)
Review: Daniel Lascar, J. E. Wallington, Stability in Model Theory (1990) (0)
A MULTIVALUED ALGEBRAIC GROUPS (2009) (0)
Saturated free algebras and almost indiscernible theories (2022) (0)
On the Existence of $\varnothing$-Definable Normal Subgroups of a Stable Group (1989) (0)
Remarks on generic stability , homogeneous pregeometries , and quasi-minimality (2009) (0)
1-based theories — the main gap fora-models (1995) (0)
ALLEN, B., Arithmetizing Uniform NC BASARAB, SA, Relative elimination of quantifiers for Hen-selian valued fields BUSS, SR, The undecidability of k-provability GALLIER, JH, What's so special about Kruskal's theorem and (1991) (0)
N ov 2 01 9 Definable f-Generic Groups over p-Adic Numbers (2019) (0)
Superrosy dependent groups having nitely satis able generics (2007) (0)
Continuous stable regularity (2021) (0)
Galois groups of large fields with simple theory (2020) (0)
Model Theory: groups, geometry, and combinatorics (2013) (0)
The models of a non-multidimensional $\omega $-stable theory (1982) (0)
Topological dynamics and the complexity of strong types (2018) (0)
Review: Ehud Hrushovski, Boris Zilber, Zariski Geometries (1999) (0)
On definable groups in real closed fields with a generic derivation, and related structures (2022) (0)

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