Kentaro Fujimoto (Bristol)
One Disanalogy between Truth Theories over Arithmetic and
over Set Theory

Some interesting disanalogies between second-order arithmetic and second-order set theory were found recently. Some of them are caused by the presence of replacement axiom (equivalently, reflection schema) in set theory.

In my talk, I will show that a theory with impredicative strength over arithmetic becomes equivalent over set theory to a theory with predicative strength over arithmetic. This disanalogy is also caused by the replacement axioms.