Kentaro Fujimoto (Bristol)

Some interesting disanalogies between secondorder arithmetic and secondorder 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. 