Research in Mathematical Logic
Alan Mathison Turing
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. For details of how to apply to such a fellowship at Manchester click here.
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
- Model theoretic methods in real algebraic geometry
- 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
