An axiomatic theory of truth is a formal deductive theory where the property of a sentence being true is treated as a primitive undefined predicate. Logical properties of many axiom systems for the truth predicate have been discussed in the context of the so-called truth-theoretic deflationism, i.e. a view according to which truth is a ‘thin’ or ‘innocent’ property without any explanatory or justificatory power with respect to non-semantic facts.
I will discuss the state of the art concerning proof-theoretic and model-theoretic properties of the most commonly studied axiomatic theories of truth (typed and untyped, both disquotational and compositional ones), focusing in particular on the problem of syntactic and semantic conservativeness of truth theories over a base (arithmetical) theory (treated mostly as a theory of syntax). I will relate the results to the research on satisfaction classes in models of arithmetic, and if the time allows, to analysis of some semantic paradoxes.

(The talk previously scheduled for this time has been canceled due to visa issues.)