Research in Mathematical Logic

There is a strong tradition in mathematical logic at Manchester. The first logician at Manchester was Alan Turing, now considered to be the father of artificial intelligence and one of the great visionaries of the twentieth century. Turing was followed at Manchester by his former student Robin Gandy who made important contributions to the foundations of proof theory and constructive mathematics. Two of Gandy's students have held chairs in at Manchester, Mike Yates (now retired), and Jeff Paris.

There are strong links with other parts of pure mathematics and with computer science.

The logic group offers opportunities for PhD study in all the research areas mentioned below, as well as a one year taught MSc programme.

Special opportunity

3 year PhD Research Fellowships. The Logic Group is taking part in the MALOA project, providing funding for PhD studies to suitably qualified applicants from non UK countries. See the MALOA website http://www.logique.jussieu.fr/MALOA/index.html for further information.

Research topics

Our research interests can be roughly listed as follows.

• Uncertain Reasoning
• Computation in Groups and Semigroups
• Model theory
  • Modules and categories
  • o-minimal structures
  • Real closed rings and fields
  • Groups of Finite Morley Rank

Members of staff involved

NAME		Title	EMAIL @manchester.ac.uk	PHONE	LOCATION
Borovik	Alexandre	Prof.	Alexandre.Borovik	0161 30 63645	2.125
Jones	Gareth	Dr.	Gareth.Jones-3		2.219
Kambites	Mark	Dr.	Mark.Kambites	0161 30 63211	2.144
Paris	Jeff B	Prof.	Jeff.Paris	0161 27 55880	2.206
Prest	Mike	Prof.	MPrest	0161 27 55875	1.120
Simmons	Harold	Dr.	H.Simmons		1.115
Tressl	Marcus	Dr.	Marcus.Tressl	0161 30 63672	2.118
Vencovská	Alena	Dr	Alena.Vencovska	0161 27 55877	2.132
Wilkie	Alex J	Prof.	Alex.Wilkie	0161 27 55858	2.145
Wilmers	George M	Dr	George.Wilmers	0161 27 55878	2.214

Research activities

Books published by members of staff include:

• M. Prest, Purity, Spectra and Localisation, Encylopedia of Mathematics and its Applications, Vol. 121, Cambridge University Press, 2009, (xxviii+769pp.).
• T. Altinel, A. Borovik and G. Cherlin. Simple Groups of Finite Morley Rank, Amer. Math. Soc. Monographs Series, Amer. Math. Soc., Providence, RI, 2008. Approx. 556 pp. ISBN-10: 0-8218-4305-2, ISBN-13: 978-0-8218-4305-5.
• A. Borovik and A. Nesin, Groups of Finite Morley Rank, Oxford University Press, 1994. xi+409 pp.
• M. Prest and J. Humphreys, Numbers, Groups and Codes, Cambridge University Press, 1989 (288pp). A second, considerably revised edition was published in 2004
• J. B. Paris, The Uncertain Reasoner's Companion: A Mathematical Perspective, Cambridge University Press, 1994.
• P. Aczel, H. Simmons and S. S. Wainer, eds. Proof theory : a selection of papers from the Leeds Proof Theory Programme, 1990, Cambridge University Press, 1992
• P. Aczel. Non-well-founded sets. Number 14 in Lecture Notes: Center for the Study of Language and Information, Stanford, CA, 1988.
• M. Prest, Model Theory and Modules, London Mathematical Society Lecture Notes Series Vol. 130, Cambridge University Press, Cambridge, 1988 (400pp).

Recent conferences organized by members of staff include:

• MIMS Workshop "New Direction in Philosophy of Mathematics", Manchester, October 2008.
• Logic Colloquium 2008
• MODNET summer school, July 2008
• British Logic Colloquium 2006
• Constructive Mathematics Day, 9 Dec. 2005
• Real Algebraic and Analytic Geometry, September 2005
• Turing 2004: A celebration of his life and achievements
• British Logic Colloquium 2001