Philosophy of Mathematics seminar




Albert Visser, Utrecht
What is a Provability Predicate?
What is a good predicate of provability? In my talk, I will discuss
the Kreisel approach to this question, the HilbertBernaysLöb 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.

