Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Computer Science Logic

CSL 1994: Computer Science Logic pp 527–541Cite as

A bounded set theory with Anti-Foundation Axiom and inductive definability

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 933))

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. P.Aczel, Non-well-founded sets, CSLI LN N14, Stanford, 1988.

    Google Scholar 

  2. P.Aczel, Introduction to the theory of inductive definitions, in: Handbook of Math. Logic, J.Barwise ed., North-Holland, Amsterdam, 1977.

    Google Scholar 

  3. J.Barwise, Admissible sets and structures. Berlin, Springer, 1975

    Google Scholar 

  4. G.Jäger. Theories for admissible sets. A unifying approach to proof theory, Studies in Proof Theory, Lecture Notes 2, Bibliopolis, 1986.

    Google Scholar 

  5. S.Feferman, Formal theories for transfinite iterations of generalized inductive definitions and some subsystems of analysis, In: Intuitionism and Proof Theory, eds. A.Kino, et al., Amsterdam, North-Holland, 1970, 303–326.

    Google Scholar 

  6. T.Fernando, A Primitive recursive set theory and AFA: on the logical complexity of the largest bisimulation, Report CS-R9213 ISSN 0169-118XCWI P.O.Box 4079, 1009 AB Amsterdam. The Netherlands.

    Google Scholar 

  7. R.O.Gandy, Set-theoretic functions for elementary syntax, in: Proc. in Pure Math., Vol 13, Part II (1974) 103–126.

    Google Scholar 

  8. Y.Gurevich, Algebras of feasible functions, in: FOCS'83 (1983) 210–214.

    Google Scholar 

  9. Y.Gurevich, Towards logic tailored for computational complexity, in: LNM 1104, Springer, Berlin (1984) 175–216.

    Google Scholar 

  10. Y.Gurevich and S.Shelah, Fixed point extensions of first-order logic, Ann. Pure Appl. Logic 32 (1986) 265–280.

    Article  Google Scholar 

  11. N.Immerman, Relational queries computable in polynomial time, in: 14th. STOC (1982) 147–152; cf. Inform. and Control 68 (1986) 86–104.

    Google Scholar 

  12. R.B. Jensen, The fine structure of the constructible hierarchy, Ann.Math. Logic 4 (1972) 229–308.

    Article  Google Scholar 

  13. A.B.Livchak, Languages of polynomial queries, in: Raschet i optimizacija teplotehnicheskih ob'ektov s pomosh'ju EVM, Sverdlovsk, 1982, 41 (in Russian).

    Google Scholar 

  14. Y.N. Moschovakis, Elementary Induction on Abstract Structures, Amsterdam, North-Holland, 1974.

    Google Scholar 

  15. E.Mendelson Introduction to Mathematical Logic, D. Van Nostrand, Princeton, 1964.

    Google Scholar 

  16. V.Yu.Sazonov, Polynomial computability and recursivity in finite domains. EIK, 16, N7 (1980) 319–323.

    Google Scholar 

  17. V.Yu.Sazonov, Bounded set theory and polynomial computability. Conf. on Applied Logic, Novosibirsk, 1985, 188–191. (In Russian)

    Google Scholar 

  18. V.Yu.Sazonov, Collection principle and existetial quantifier. (In Russian) Vychislitel'nye sistemy 107 (1985) Novosibirsk, 30–39.) (Cf. English translation in AMS Transi. (2) 142 (1989) 1–8.)

    Google Scholar 

  19. V.Yu.Sazonov, Bounded set theory, polynomial computability and Δ-programming, Vychislitel'nye sistemy 122 (1987) Novosibirsk, 110–132 (in Russian). Cf. also LNCS 278 (1987) 391–397 (in English).

    Google Scholar 

  20. V.Yu.Sazonov, Bounded Set Theory and Inductive Definability, Logic Colloquium'90, JSL, 56, Nu.3 (1991) 1141–1142.

    Google Scholar 

  21. V.Yu.Sazonov, Hereditarily-finite sets, data bases and polynomial-time computability, TCS 119 (1993) 187–214, Elsevier.

    Google Scholar 

  22. M.Y.Vardi, The complexity of relational query languages, STOC'82, 137–146.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Program Systems Institute, 152140, Pereslavl-Zalessky, Russia

    Vladimir Yu. Sazonov

Authors
  1. Vladimir Yu. Sazonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Leszek Pacholski Jerzy Tiuryn

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Sazonov, V.Y. (1995). A bounded set theory with Anti-Foundation Axiom and inductive definability. In: Pacholski, L., Tiuryn, J. (eds) Computer Science Logic. CSL 1994. Lecture Notes in Computer Science, vol 933. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022280

Download citation

  • DOI: https://doi.org/10.1007/BFb0022280

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60017-6

  • Online ISBN: 978-3-540-49404-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation