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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 @


Model theory
Stability theory
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

Ricardo Bello Aguirre (2012)
David Bradley-Williams (2009)
Erick Garcia Ramirez (2013)
Daoud Siniora (2013)
Daniel Wolf (2012)


Garcia D, Macpherson D, Steinhorn C Pseudofinite structures and simplicity Journal of Mathematical Logic, 15, 2015
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Macpherson HD; Aschenbrenner M; Dolich A; Haskell D; Starchenko S Vapnik-Chervonenkis density in some theories without the independence property, I. 2013

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

Lockett DC, Macpherson HD Orbit-equivalent infinite permutation groups Journal of Algebraic Combinatorics, 1-16, 2013
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Macpherson HD, Tent K Pseudofinite groups with NIP theory and definability in finite simple groups In Groups and model theory, 576, 255-267, 2012
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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
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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
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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
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Macpherson HD, Tent K Simplicity of some automorphism groups Journal of Algebra, 342, 40-52, 2011
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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

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

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

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

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

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

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

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

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

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

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

Macpherson HD, Aschenbrenner M, Dolich A, Haskell D, Starchenko S Vapnik-Chervonenkis density in some theories without the independence property,I Transactions of the American Mathematical Society

Bodirsky M, Macpherson HD Reducts of structures and maximal-closed permutation groups Journal of Symbolic Logic
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