Bounded arithmetic in free logic (Proof theory and complexity)
Yoriyuki Yamagata · Institutional Repositories DataBase (IRDB) · 2013
One of the central open questions in bounded arithmetic is whether Buss' hierarchy of theories of bounded arithmetic collapses or not.In this resume, we summarize the author's recent attempt to this problem.We reformulate Buss' theories using free logic and conjecture that such theories are easier to handle.To support this claim, the author first shows that Buss' theories prove consistencies of induction-free fragments of our theories whose formulae have bounded complexity.Next, the author proves that although our theories are based on an apparently weaker logic, we can interpret theories in Buss' hierarchy by our theories using a simple translation.