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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
View abstract

García D, Macpherson D, Steinhorn C Pseudofinite structures and simplicity Journal of Mathematical Logic, 15, 2015
DOI:10.1142/S0219061315500026
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

Macpherson HD, Tent K Simplicity of some automorphism groups Journal of Algebra, 342, 40-52, 2011
DOI:10.1016/j.jalgebra.2011.05.021
View abstract

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
View abstract

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
View abstract

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
View abstract

Herwig B, Macpherson HD, Martin G, Nurtazin A, Truss JK Onא0-categorical weakly o-minimal structures Annals of Pure and Applied Logic, 101, 65-93, 2000
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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

Droste M, Macpherson D, Sauer N, Giraudet M Set-Homogeneous Graphs Journal of Combinatorial Theory, Series B, 62, 63-95, 1994
DOI:10.1006/jctb.1994.1055
View abstract

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
View abstract

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
View abstract

Macpherson D Maximal subgroups of infinite dimensional general linear groups Journal of the Australian Mathematical Society, 53, 338-351, 1992
DOI:10.1017/S144678870003651X
View abstract

Macpherson D, Woodrow R The permutation group induced on a moiety Forum Mathematicum, 4, 243-256, 1992
DOI:10.1515/form.1992.4.243
View abstract

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
View abstract

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
View abstract

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
View abstract

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 N0-categorical groups 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
View abstract

Macpherson HD Groups of automorphisms of N0-categorical structures 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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

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
View abstract

Macpherson HD; Glass AMW New Pathways between Group Theory and Model TheoryProceedings 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