Title: Reverse mathematics and proof and model theory of arithmetic

Abstract:
Reverse mathematics program in the setting of second-order arithmetic
is often considered as a formalization of computable mathematics.
Indeed, the program is strongly developed by numerous computability
theorists with vast knowledge from various areas of computability
theory. On the other hand, the frameworks of the program, various
systems of second-order arithmetic are also studied intensively from
the viewpoints of proof theory and model theory. They are typically
useful when the required induction axioms should be carefully
examined. In this talk, I will overview the recent developments of
those and how they are combined with computability theoretic aspects.