What is a good predicate of provability? In my talk, I will discuss the Kreisel approach to this question, the Hilbert-Bernays-Löb approach and the Feferman approach. I provide some separating examples. I will demonstrate how, in the case of sequential theories with full induction, we can sidestep these approaches and define provability in a way that does not use any design choices like choice of Gödel numbering and deductive system. I will also discuss the construction of predicates that satisfy the Kreisel condition even in the case where the given theory is substantially unsound.
See the seminar webpage http://users.ox.ac.uk/~philmath/pomseminar.html for titles and abstracts of other speakers as available.
Philosophy of Mathematics Seminar Convenors: Daniel Isaacson and Volker Halbach