## Journal of Symbolic Logic

### The Friedman—Sheard programme in intuitionistic logic

#### Abstract

This paper compares the roles classical and intuitionistic logic play in restricting the free use of truth principles in arithmetic. We consider fifteen of the most commonly used axiomatic principles of truth and classify every subset of them as either consistent or inconsistent over a weak purely intuitionistic theory of truth.

#### Article information

Source
J. Symbolic Logic, Volume 77, Issue 3 (2012), 777-806.

Dates
First available in Project Euclid: 13 August 2012

https://projecteuclid.org/euclid.jsl/1344862162

Digital Object Identifier
doi:10.2178/jsl/1344862162

Mathematical Reviews number (MathSciNet)
MR2987138

Zentralblatt MATH identifier
1248.03081

#### Citation

Leigh, Graham E.; Rathjen, Michael. The Friedman—Sheard programme in intuitionistic logic. J. Symbolic Logic 77 (2012), no. 3, 777--806. doi:10.2178/jsl/1344862162. https://projecteuclid.org/euclid.jsl/1344862162

#### References

• A. Cantini A theory of formal truth arithmetically equivalent to ${\rm ID}\sb 1$, Journal of Symbolic Logic, vol. 55(1990), no. 1, pp. 244–259.
• S. Feferman Toward useful type-free theories. I, Journal of Symbolic Logic, vol. 49(1984), no. 1, pp. 75–111.
• –––– Reflecting on incompleteness, Journal of Symbolic Logic, vol. 56(1991), no. 1, pp. 1–49.
• H. Friedman and M. Sheard An axiomatic approach to self-referential truth, Annals of Pure and Applied Logic, vol. 33(1987), no. 1, pp. 1–21.
• V. Halbach A system of complete and consistent truth, Notre Dame Journal of Formal Logic, vol. 35(1994), no. 3, pp. 311–327.
• S. A. Kripke Semantical considerations on modal logic, Acta Philosophica Fennica, vol. 16(1963), pp. 83–94.
• G. E. Leigh Proof-theoretic investigations into the Friedman-Sheard theories and other theories of truth, Ph.D. thesis, University of Leeds,2010.
• G. E. Leigh and M. Rathjen An ordinal analysis for theories of self-referential truth, Archive for Mathematical Logic, vol. 49(2010), no. 2, pp. 213–247.
• V. McGee How truthlike can a predicate be? A negative result, Journal of Philosophical Logic, vol. 14(1985), no. 4, pp. 399–410.
• A. S. Troelstra and D. van Dalen Constructivism in mathematics. Vol. I, Studies in Logic and the Foundations of Mathematics, vol. 121, North-Holland, Amsterdam,1988.