Advertisement

A primitive recursive set theory and AFA: On the logical complexity of the largest bisimulation

  • Tim Fernando
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 626)

Abstract

A subsystem of Kripke-Platek set theory proof-theoretically equivalent to primitive recursive arithmetic is isolated; Aczel's (relative) consistency argument for the Anti-Foundation Axiom is adapted to a (related) weak setting; and the logical complexity of the largest bisimulation is investigated.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Samson Abramsky. Topological aspects of non-well-founded sets. Handwritten notes.Google Scholar
  2. 2.
    Peter Aczel. An introduction to inductive definitions. In J. Barwise, editor. Handbook of Mathematical Logic. North-Holland, Amsterdam, 1977.Google Scholar
  3. 3.
    Peter Aczel. The type-theoretic interpretation of constructive set theory. In Logic Colloquium '77. North-Holland, Amsterdam, 1978.Google Scholar
  4. 4.
    Peter Aczel. Non-well-founded sets. CSLI Lecture Notes Number 14, Stanford, 1988.Google Scholar
  5. 5.
    Jon Barwise. Admissible sets and structures. Springer-Verlag, Berlin, 1975.Google Scholar
  6. 6.
    Jon Barwise and John Etchemendy. The liar: an essay on truth and circularity. Oxford University Press, Oxford, 1987.Google Scholar
  7. 7.
    Solomon Feferman. Predicatively reducible systems of set theory. In Proc. Symp. Pure Math., vol 13, Part II. Amer. Math. Soc., Providence, R.I., 1974.Google Scholar
  8. 8.
    Solomon Feferman. A language and axioms for explicit mathematics. In J.N. Crossley, editor, Algebra and Logic, LNM 450. Springer-Verlag, Berlin, 1975.Google Scholar
  9. 9.
    Solomon Feferman. Hilbert's program relativized: proof-theoretical and foundational reductions. Journal of Symbolic Logic, 53(2), 1988.Google Scholar
  10. 10.
    Tim Fernando. Transition systems over first-order models. Manuscript, 1991.Google Scholar
  11. 11.
    Tim Fernando. Parallelism, partial execution and programs as relations on states. Manuscript, 1992.Google Scholar
  12. 12.
    Gerhard Jäger. A version of Kripke-Platek set theory which is conservative over Peano arithmetic. Zeitschr. f. math. Logik und Grundlagen d. Math, 30, 1984.Google Scholar
  13. 13.
    Gerhard Jäger. Induction in the elementary theory of types and names. Preprint, 1988.Google Scholar
  14. 14.
    R.B. Jensen and C. Karp. Primitive recursive set functions. In Proc. Symp. Pure Math., vol 13, Part I. Amer. Math. Soc., Providence, R.I., 1971.Google Scholar
  15. 15.
    Ingrid Lindström. A construction of non-well-founded sets within Martin-Löf 's type theory. Journal of Symbolic Logic, 54, 1989.Google Scholar
  16. 16.
    M. Mislove, L. Moss, and F. Oles. Non-well-founded sets obtained from ideal fixed points. In Fourth annual symposium on Logic in Computer Science, 1989.Google Scholar
  17. 17.
    Charles Parsons. On a number-theoretic choice schema and its relation to induction. In J. Myhill, editor, Intuitionism and Proof Theory. North-Holland, Amsterdam, 1970.Google Scholar
  18. 18.
    Alban Ponse. Computable processes and bisimulation equivalence. Technical Report CS-R9207, Centre for Mathematics and Computer Science, 1992.Google Scholar
  19. 19.
    J.J.M.M. Rutten. Non-well-founded sets and programming language semantics. Technical Report CS-R9063, Centre for Mathematics and Computer Science, 1990.Google Scholar
  20. 20.
    J.J.M.M. Rutten. Hereditarily finite sets and complete metric spaces. Technical Report CS-R9148, Centre for Mathematics and Computer Science, 1991.Google Scholar
  21. 21.
    Wilfried Sieg. Fragments of arithmetic. Annals of Pure and Applied Logic, 28, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Tim Fernando

There are no affiliations available

Personalised recommendations