# School of Mathematics

## Prof H Dugald Macpherson

Professor of Pure Mathematics

Pure Mathematics

### Contact details

Room: Satellite 10.25

Tel: +44 (0)113 3435166

Email: H.D.MacPherson @ leeds.ac.uk

### Keywords

Model theory

Stability theory

O-minimal

Pseudofinite

Infinite permutation group

Homogeneous structure

Valued field

Vapnik-Chervonenkis density

## Research interests

I work in model theory (mathematical logic) and adjacent areas of permutation group theory and combinatorics. Particular interests include the following.

1. Model theory of valued fields, from the viewpoint of generalised stability theory -- issues around definability in henselian fields.

2. Generalisations of o-minimality (structure theory arising from restrictions on one-variable definable sets).

3. Model theory of finite (and pseudofinite) structures -- for example, model-theoretic consequences of asymptotic uniformities on sizes of definable sets.

4. Model theory of groups -- e.g. groups in stable and simple theories, model theory of finite groups.

5. Abstract model theory -- generalisations of stability, connections to combinatorial conditions such as Vapnik-Chevonenkis density.

6. Infinite permutation groups -- often arising as automorphism groups of first order structures.

7. Homogeneous structures, in the sense of Fraisse. There are connections to permutation groups and combinatorics, and more recent connections to Ramsey theory, topological dynamics, and constraint satisfaction.

### Useful links

MALOA Initial Training Network

Personal Home Page

British Logic Colloquium

Leeds Logic Group

## Current postgraduate students

Erick Garcia Ramirez (2013)

Rosario Mennuni (2016)

Daoud Siniora (2013)

## Publications

**Bodirsky M, Macpherson D** Reducts of structures and maximal-closed permutation groups *Journal of Symbolic Logic*, **81**, 1087-1114, 2016

DOI:10.1017/jsl.2015.78

View abstract

**Macpherson HD, Aschenbrenner M, Dolich A, Haskell D, Starchenko S** Vapnik-Chervonenkis *Transactions of the American Mathematical Society*, 2016

**Macpherson D, Tent K** Profinite groups with NIP theory and p-adic analytic groups *Bulletin of the London Mathematical Society*, **48**, 1037-1049, 2016

DOI:10.1112/blms/bdw064

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**García D, Macpherson D, Steinhorn C** Pseudofinite structures and simplicity *Journal of Mathematical Logic*, **15**, 2015

DOI:10.1142/S0219061315500026

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**Pillay A, VanDenDries L, Koenigsmann J, Macpherson HD, Pillay A, Toffalori C, Wilkie AJ** Some Themes Around First Order Theories Without the Independence Property *MODEL THEORY IN ALGEBRA, ANALYSIS AND ARITHMETIC*, **2111**, 13-33, 2014

DOI:10.1007/978-3-642-54936-6_2

**Macpherson D; Toffalori C ** Model theory in Algebra, analysis and Arithmetic: A preface. **2111**, 1-11 2014

DOI:10.1007/978-3-642-54936-6_1

**Macpherson D; Toffalori C ** *Model theory in algebra, analysis and arithmetic: A preface*. 2111, 2014

DOI:10.1007/978-3-642-54936-6__1

**Lockett DC, Macpherson HD** Orbit-equivalent infinite permutation groups *Journal of Algebraic Combinatorics*, **38**, 973-988, 2013

DOI:10.1007/s10801-013-0434-0

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**Bodirsky M, Macpherson HD, Thapper J** Constraint Satisfaction Tractability from Semi-Lattice Operations on Infinite Sets *ACM TRANSACTIONS ON COMPUTATIONAL LOGIC*, **14**, 2013

DOI:10.1145/2528933

**Macpherson HD, Aschenbrenner, M, Dolich, A, Haskell, D, Starchenko, S** Vapnik-Chervonenkis density in some theories without the Independence Property, II *Notre Dame Journal of Formal Logic*, 2013

**Macpherson HD, Haskell D, Hrushovski E** Unexpected imaginaries in valued fields with analytic structure *The Journal of Symbolic Logic*, **78**, 523-542, 2013

DOI:10.2178/jsl.7802100

**Lockett DC, Macpherson HD** Orbit-equivalent infinite permutation groups *Journal of Algebraic Combinatorics*, 1-16, 2013

DOI:10.1007/s10801-013-0434-0

View abstract

**Macpherson HD, Tent K** Pseudofinite groups with NIP theory and definability in finite simple groups In *Groups and model theory*, **576**, 255-267, 2012

DOI:10.1090/comm/576/11352

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**Macpherson HD, Gray R, Praeger CE, Royle GF** Set-homogeneous directed graphs *Journal of Combinatorial Theory, Series B*, **102**, 474-520, 2011

DOI:10.1016/j.jctb.2011.08.002

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**Macpherson HD, Elwes R, Jaligot E, Ryten MJ** Groups in supersimple and pseudofinite theories *Proceedings of the London Mathematical Society*, **103**, 1049-1082, 2011

DOI:10.1112/plms/pdr002

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**Macpherson HD, Steinhorn C** Definability in classes of finite structures In *Finite and Algorithmic Model Theory*, **379**, 140-173, 2011

**Macpherson HD** A survey of homogeneous structures *Discrete Mathematics*, **311**, 1599-1634, 2011

DOI:10.1016/j.disc.2011.01.024

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**Macpherson HD, Tent K** Simplicity of some automorphism groups *Journal of Algebra*, **342**, 40-52, 2011

DOI:10.1016/j.jalgebra.2011.05.021

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**Macpherson HD, Liebeck MW, Tent K** Primitive permutation groups of bounded orbital diameter *Proceedings of the London Mathematical Society (3)*, **100**, 216-248, 2009

DOI:10.1112/plms/pdp024

**Macpherson HD, Gray R** Countable connected-homogeneous graphs *Journal of Combinatorial Theory, Series B*, **100**, 97-118, 2009

DOI:10.1016/j.jctb.2009.04.002

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**Macpherson HD, Elwes R** A survey of asymptotic classes and measurable structures In *Model theory with applications to algebra and analysis*, **350**, 125-159, 2008

**Macpherson HD, Steinhorn C** One-dimensional asymptotic classes of finite structures *Transactions of the American Mathematical Society*, **360**, 411-448, 2007

**Macpherson HD; Steinhorn C ** One-dimensional asymptotic classes of finite structures. 2007

DOI:10.1090/S0002-9947-07-04382-6

**Haskell D; Hrushovski E; Macpherson HD ** *Stable domination and independence in algebraically closed valued fields*. Cambridge University Press 2007

**Haskell D, Hrushovski E, Macpherson HD** Definable sets in algebraically closed valued fields: elimination of imaginaries *Journal für die Reine und Angewandte Mathematik*, **2006**, 175-236

DOI:10.1515/CRELLE.2006.066

**Macpherson HD, Tent K** Stable pseudofinite groups *Journal of Algebra*, 2006

**Kudaibergenov K, Macpherson HD** On model companions for structures with an automorphism *Siberian Advances in Mathematics*, **63**, 63-78, 2006

**Bhattacharjee M, Macpherson HD** Jordan groups and limits of betweenness relations *Journal of Group Theory*, **9**, 59-94, 2006

DOI:10.1515/JGT.2006.004

**Barbina S, Macpherson HD** Reconstruction of homogeneous relational structures *Journal of Symbolic Logic*, 2005

**Macpherson HD, Thomas S** Comeagre conjugacy classes and free products with amalgamation *Discrete Mathematics*, **291**, pp.135--142, 2005

DOI:10.1016/j.disc.2004.04.025

**Bhattacharjee M, Macpherson HD** A locally finite dense group acting on the random graph *Forum Mathematicum*, **17**, 513-517, 2005

DOI:10.1515/form.2005.17.3.513

**Kulpeshov BS, Macpherson HD** Minimality conditions on circularly ordered structures *MATH LOGIC QUART*, **51**, 377-399, 2005

DOI:10.1002/malq.200410040

**Haskell D, Macpherson HD** Definable sets in valued fields In *Model theory and applications*, **11**, 117-149, 2005

**Herwig BF, Hrushovski E, Macpherson HD** Interpretable groups, stably embedded sets and Vaughtian pairs *Journal of London Mathematical Society*, **68**, 1-11, 2003

**Bhattacharjee M, Macpherson HD** Strange permutation represntations of free groups *Journal of the Australian Mathematical Society. Series B. Applied Mathematics*, **74**, 267-285, 2003

**Droste M, Macpherson D, Mekler A** Uncountable homogeneous partial orders *Mathematical Logic Quarterly*, **48**, 525-532, 2002

DOI:10.1002/1521-3870(200211)48:4<525::AID-MALQ525>3.0.CO;2-3

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**Droste M, Macpherson HD, Mekler AH** Uncountable homogenous partial orders *Mathematical Logic Quarterly*, **48**, 525-532, 2002

**Droste M, Macpherson D** The automorphism group of the universal distributive lattice *Algebra Universalis*, **43**, 295-306, 2000

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**Herwig B, Macpherson HD, Martin G, Nurtazin A, Truss JK** Onא*Annals of Pure and Applied Logic*, **101**, 65-93, 2000

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**Macpherson HD, Mosley A, Tent K** Permutation groups in o-minimal structures *Journal of London Mathematical Society*, 2000

**Macpherson HD, Marker D, Steinhorn C** Weakly o-minimal structures and real closed fields *Transactions of the American Mathematical Society*, **352**, 5435-5483, 2000

**Ivanov AA, Macpherson D** Strongly determined types *Annals of Pure and Applied Logic*, **99**, 197-230, 1999

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**Van Den Dries L, Haskell D, Macpherson D** One-dimensional p-adic subanalytic sets *Journal of the London Mathematical Society*, **59**, 1-20, 1999

**Macpherson HD, van den Dries L, Haskell D** One-dimensional p-adic subanalytic sets *Journal of London Mathematical Society*, **59**, 1-20, 1999

**Haskell D, Macpherson D** A note on valuation definable expansions of fields *Journal of Symbolic Logic*, **63**, 739-743, 1998

**Droste M, Giraudet M, Macpherson D** Set-Homogeneous Graphs and Embeddings of Total Orders *Order*, **14**, 9-20, 1997

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**Haskell D, Macpherson D** A version of o-minimality for the p-adics *Journal of Symbolic Logic*, **62**, 1075-1092, 1997

**Macpherson D, Steinhorn C** Extending partial orders on o-minimal structures to definable total orders *Mathematical Logic Quarterly*, **43**, 456-464, 1997

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**Archer R, Macpherson D** Soluble omega-categorical groups *Mathematical Proceedings of the Cambridge Philosophical Society*, **121**, 219-227, 1997

**Guralnick RM, Liebeck MW, Macpherson HD, Seitz GM** Modules for algebraic groups with finitely many orbits on subspaces *Journal of Algebra*, **196**, 211-250, 1997

**Macpherson D** Sharply multiply homogeneous permutation groups, and rational scale types *Forum Mathematicum*, **8**, 501-507, 1996

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**Macpherson HD, Steinhorn C** On variants of o-minimality *Annals of Pure and Applied Logic*, **79**, 165-209, 1996

**Adeleke SA, Macpherson D** Classification of infinite primitive Jordan permutation groups *Proceedings of the London Mathematical Society*, **72**, 63-123, 1996

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**Macpherson D, Praeger CE** Cycle Types in Infinite Permutation Groups *Journal of Algebra*, **175**, 212-240, 1995

DOI:10.1006/jabr.1995.1184

**Droste M, Giraudet M, Macpherson D** Periodic ordered permutation groups and cyclic orderings *Journal of Combinatorial Theory, Series B*, **63**, 310-321, 1995

DOI:10.1006/jctb.1995.1022

**Haskell D, Macpherson D** Cell decompositions of C-minimal structures *Annals of Pure and Applied Logic*, **66**, 113-162, 1994

DOI:10.1016/0168-0072(94)90064-7

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**Droste M, Giraudet M, Macpherson D, Sauer N** Set-homogeneous graphs *Journal of Combinatorial Theory, Series B*, **62**, 63-95, 1994

DOI:10.1006/jctb.1994.1055

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**Macpherson D, Praeger CE** Infinitary Versions of the O’Nan—Scott Theorem *Proceedings of the London Mathematical Society*, **s3-68**, 518-540, 1994

DOI:10.1112/plms/s3-68.3.518

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**Macpherson D** Maximal subgroups of infinite dimensional general linear groups *Journal of the Australian Mathematical Society*, **53**, 338-351, 1992

DOI:10.1017/S144678870003651X

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**Macpherson D, Woodrow R** The permutation group induced on a moiety *Forum Mathematicum*, **4**, 243-256, 1992

DOI:10.1515/form.1992.4.243

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**Droste M, Macpherson HD** On k-homogeneous posets and graphs *Journal of Combinatorial Theory, Series A*, **56**, 1-15, 1991

DOI:10.1016/0097-3165(91)90018-C

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**Macpherson D** Finite axiomatizability and theories with trivial algebraic closure *Notre Dame Journal of Formal Logic*, **32**, 188-192, 1991

DOI:10.1305/ndjfl/1093635744

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**Macpherson D, Mekler AH, Shelah S** The number of infinite substructures *Mathematical Proceedings of the Cambridge Philosophical Society*, **109**, 193-209, 1991

DOI:10.1017/S0305004100069668

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**Hodges W, Hodkinson IM, Macpherson D** Omega-categoricity, relative categoricity and coordinatisation *Annals of Pure and Applied Logic*, **46**, 169-199, 1990

DOI:10.1016/0168-0072(90)90033-X

**Macpherson HD** Maximal subgroups of infinite symmetric groups *Journal of the London Mathematical Society*, **s2-42**, 85-92, 1990

DOI:10.1112/jlms/s2-42.1.85

**Macpherson HD** Subgroups of infinite symmetric groups *Journal of the London Mathematical Society*, **s2-42**, 64-84, 1990

DOI:10.1112/jlms/s2-42.1.64

**Macpherson HD** Absolutely ubiquitous structures and N*Quarterly Journal of Mathematics*, **39**, 483-500, 1988

DOI:10.1093/qmath/39.4.483

**Macpherson HD** Infinite Permutation Groups of Rapid Growth *Journal of the London Mathematical Society*, **s2-35**, 276-286, 1987

DOI:10.1112/jlms/s2-35.2.276

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**Macpherson HD** Groups of automorphisms of N*Quarterly Journal of Mathematics*, **37**, 449-465, 1986

DOI:10.1093/qmath/37.4.449

**Macpherson HD** Homogeneity in infinite permutation groups *Periodica Mathematica Hungarica*, **17**, 211-233, 1986

DOI:10.1007/BF01848649

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**Macpherson HD** Graphs determined by their finite induced subgraphs *Journal of Combinatorial Theory, Series B*, **41**, 230-234, 1986

DOI:10.1016/0095-8956(86)90046-8

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**Macpherson HD** Orbits of infinite permutation groups *Proceedings of the London Mathematical Society*, **s3-51**, 246-284, 1985

DOI:10.1112/plms/s3-51.2.246

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**Macpherson HD** Growth rates in infinite graphs and permutation groups *Proceedings of the London Mathematical Society*, **s3-51**, 285-294, 1985

DOI:10.1112/plms/s3-51.2.285

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**Cameron PJ, Macpherson HD** Rank three permutation groups with rank three subconstituents *Journal of Combinatorial Theory, Series B*, **39**, 1-16, 1985

DOI:10.1016/0095-8956(85)90034-6

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**MACPHERSON HD** GROWTH-RATES IN INFINITE-GRAPHS AND PERMUTATION-GROUPS *PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY*, **51**, 285-294, 1985

**MACPHERSON HD** ORBITS OF INFINITE PERMUTATION-GROUPS *PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY*, **51**, 246-284, 1985

**MACPHERSON HD** THE ACTION OF AN INFINITE PERMUTATION GROUP ON UNORDERED SUBSETS OF A SET *PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY*, **46**, 471-486, 1983

**Macpherson HD** The action of an infinite permutation group on unordered subsets of a set *Proceedings of the London Mathematical Society*, **S3-46**, 471-486, 1983

DOI:10.1112/plms/s3-46.3.471

**Macpherson HD** Infinite distance transitive graphs of finite valency *Combinatorica*, **2**, 63-69, 1982

DOI:10.1007/BF02579282

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Macpherson HD; Glass AMW *New Pathways between Group Theory and Model Theory*Proceedings of the Muelheim conference“New Pathways between Group Theory and Model Theory

**Macpherson HD** Model theory of finite and pseudofinite groups *Archive for Mathematical Logic*

DOI:10.1007/s00153-017-0584-1

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