Restricted truth predicates in first-order logic
Thomas Bolander · 2002
Introduction It is well-known that there exist consistent first-order theories that become inconsistent when we add Tarski's schema T. This is Tarski's Theorem. To avoid the inconsistency result, one can restrict Tarski's schema in di#erent ways. In our paper we restrict Tarski's schema T by only instantiating the schema with a proper subset of the set of all sentences. We prove several results concerning the sets of sentences M for which Tarski's schema T instantiated with the sentences of M is relatively consistent with any first-order theory. Let be any first-order language containing the one-place predicate symbol T (intended to denote truth). Let M be a subset of the set of sentences of L. By the truth predicate over M we understand the instances over M of Tarski's schema T, that is, the theory where ## is some suitable coding scheme. Such theories are also called restricted truth predicates. Let - denote the first-order language with the predicate symbol T rem