Logical Approaches to Computational Barriers

A Classification of Axiomatic Theories of Truth

Speaker:
| Graham Leigh |

Slot: |
Array, 11:20-11:40, col. 5 |

We augment the first-order language of Peano Arithmetic with a unary predicate $T$ with $T(x)$ intended to mean ``$x$ is the G"odel number of a true sentence of arithmetic''. In (1987) Friedman and Sheard constructed a list of twelve axioms and rules of inference concerning the predicate $T$, each expressing some desirable property of truth, and classified all subsets of the list as either consistent or inconsistent. This gave rise to a collection of nine theories of truth, two of which have been treated in the literature (see Friedman and Sheard 1987, Halbach (1994), Sheard (2001) and Cantini (1990) for more details). We uncover the proof-theoretic strength of the remaining seven and in the process construct a proof-theory of truth allowing the systems to be subject to an ordinal analysis. (1987) H. Friedman and M. Sheard, An axiomatic approach to self-referential truth, Annals of Pure and Applied Logic, 33 1--21. (1990) A. Cantini, A theory of formal truth arithmetically equivalent to ID1, Journel of Symbolic Logic, 55, 1, 244--259. (1994) V. Halbach, A system of complete and consistent truth, Notre Dame Journel of Formal Logic, vol. 35, 3. (2001) M. Sheard, Weak and strong theories of truth, Studia Logica, 68, 89--101.

websites: Arnold Beckmann | 2008-05-28 |