Studia Logica

, Volume 68, Issue 1, pp 89–101 | Cite as

Weak and Strong Theories of Truth

  • Michael Sheard

Abstract

A subtheory of the theory of self-referential truth known as FS is shown to be weak as a theory of truth but equivalent to full FS in its proof-theoretic strength.

truth FS 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Cantini, A., 'A theory of formal truth arithmetically equivalent to ID 1', Journal of Symbolic Logic 55 (1990), 244-259.Google Scholar
  2. [2]
    Feferman, S., 'Theories of finite type related to mathematical practice', in J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, 1977, pp. 913-971.Google Scholar
  3. [3]
    Feferman, S., 'Reflecting on incompleteness', Journal of Symbolic Logic 56 (1991), 1-49.Google Scholar
  4. [4]
    Friedman, H., and M. Sheard, 'An axiomatic approach to self-referential truth', Annals of Pure and Applied Logic 33 (1987), 1-21.Google Scholar
  5. [5]
    Friedman, H., and M. Sheard, 'The disjunction and existence properties for axiomatic systems of truth', Annals of Pure and Applied Logic 40 (1988), 1-10.Google Scholar
  6. [6]
    Halbach, V., 'A system of complete and consistent truth', Notre Dame Journal of Formal Logic 35 (1994), 311-327.Google Scholar
  7. [7]
    Kotlarski, H., and Z. Ratajczyk, 'More on induction in the language with a full satisfaction class', Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 36 (1990), 441-454.Google Scholar
  8. [8]
    McGee, V., 'How truth-like can a predicate be? A negative result', Journal of Philosophical Logic 14 (1985), 399-410.Google Scholar
  9. [9]
    Pohlers, W., 'Subsystems of set theory and second order number theory', in S. R. Buss (ed.), Handbook of Proof Theory, Elsevier, 1998, pp. 209-335.Google Scholar
  10. [10]
    SchÜtte, K., Proof Theory, Springer-Verlag, 1977.Google Scholar
  11. [11]
    Sheard, M., 'A guide to truth predicates in the modern era', Journal of Symbolic Logic 59 (1994), 1032-1054.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Michael Sheard
    • 1
  1. 1.Department of MathematicsSt. Lawrence UniversityCanton

Personalised recommendations