Mathematical Logic

Alan Turing
Alan 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.

We have strong links with other parts of pure mathematics and with computer science.

We offer opportunities for PhD study in all the research areas mentioned below (for admissions please visit here), as well as a one year taught MSc programme.

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).

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We have strong links with other parts of pure mathematics and with computer science
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