Peter Aczel

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Peter Aczel
Aczel Rathjen.jpg
Peter Aczel (left) with Michael Rathjen, Oberwolfach 2004
Born Peter Henry George Aczel
(1941-10-31) 31 October 1941 (age 75)
Alma mater University of Oxford
Thesis Mathematical problems in logic (1967)
Doctoral advisor John Newsome Crossley
Doctoral students
  • Joao Filipe Castel-Branco Belo[1]
  • Christopher Martin Fox[2]
  • Nicola Gambino[3]
  • Gilles Jacques Barthe[4]
  • George Koletsos[5]
  • Jouko Antero Väänänen[6]
Known for Aczel's anti-foundation axiom

Peter Henry George Aczel (born October 31, 1941) is a British mathematician, logician and Emeritus joint Professor in the School of Computer Science and the School of Mathematics at the University of Manchester.[7] He is known for his work in non-well-founded set theory,[8] constructive set theory,[9][10] and Frege structures.[11][12][13]


Aczel completed his Bachelor of Arts in Mathematics in 1963[14] followed by a DPhil at the University of Oxford in 1966 under the supervision of John Crossley.[7][15]

Career and research[edit]

After two years of visiting positions at the University of Wisconsin–Madison and Rutgers University Aczel took a position at the University of Manchester. He has also held visiting positions at the University of Oslo, California Institute of Technology, Utrecht University, Stanford University and Indiana University Bloomington.[14] He was a visiting scholar at the Institute for Advanced Study in 2012.[16]

Aczel is on the editorial board of the Notre Dame Journal of Formal Logic[17] and the Cambridge Tracts in Theoretical Computer Science, having previously served on the editorial boards of the Journal of Symbolic Logic and the Annals of Pure and Applied Logic.[14][18]


  1. ^ Belo, Joao Filipe Castel-Branco (2008). Foundations of dependently sorted logic (PhD thesis). University of Manchester. Archived from the original on 2012-12-23. 
  2. ^ Fox, Christopher Martin (2005). Point-set and point-free topology in constructive set theory (PhD thesis). University of Manchester. [dead link]
  3. ^ Gambino, Nicolas (2002). Sheaf interpretations for generalised predicative intuitionistic systems (PhD thesis). University of Manchester. [dead link]
  4. ^ Barthe, Gilles Jacques (1993). Term declaration logic and generalised composita (PhD thesis). University of Manchester. [dead link]
  5. ^ Koletsos, George (1980). Functional interpretation and β-logic (PhD thesis). University of Manchester. [dead link]
  6. ^ Väänänen, Jouko Antero (1977). Applications of set theory to generalised quantifiers (PhD thesis). University of Manchester. [dead link]
  7. ^ a b Peter Aczel at the Mathematics Genealogy Project
  8. ^
  9. ^ Aczel, P. (1977). "An Introduction to Inductive Definitions". Handbook of Mathematical Logic. Studies in Logic and the Foundations of Mathematics. 90. pp. 739–201. doi:10.1016/S0049-237X(08)71120-0. ISBN 9780444863881. 
  10. ^ Aczel, P.; Mendler, N. (1989). "A final coalgebra theorem". Category Theory and Computer Science. Lecture Notes in Computer Science. 389. p. 357. doi:10.1007/BFb0018361. ISBN 3-540-51662-X. 
  11. ^ Aczel, P. (1980). "Frege Structures and the Notions of Proposition, Truth and Set". The Kleene Symposium. Studies in Logic and the Foundations of Mathematics. 101. pp. 31–32. doi:10.1016/S0049-237X(08)71252-7. ISBN 9780444853455. 
  12. ^ Peter Aczel publications in Google Scholar
  13. ^ Peter Aczel at DBLP Bibliography Server
  14. ^ a b c Peter Aczel page the University of Manchester
  15. ^ Aczel, Peter (1966). Mathematical problems in logic (DPhil thesis). University of Oxford. (subscription required)
  16. ^ Institute for Advanced Study: A Community of Scholars
  17. ^ Notre Dame Journal of Formal Logic
  18. ^ Annals of Pure and Applied Logic