Oberseminar "Mathematische Logik" - PD Dr. Martin Fischer

Feferman introduced the notion of reflective closure in 1991. The reflective closure was intended to capture the implicit commitments of accepting a theory. For PA the reflective closure turned out to be proof-theoretically equivalent to the predicative systems of ramified analysis. The use of a type-free truth predicate was later described as `artificial’ and one of the reasons for Feferman to restate the reflective closure in terms of his program of unfolding. In the talk I will provide some philosophical background on the notion of reflective closure. Based on this I will take another look at the options for a type-free truth predicate in the setting of partial logic to be less `artificial’ for the formulation of reflective closure and at the same time recapture the proof-theoretic strength of the classical versions.