Time:  12:00  13:20 
Room: 
Doherty Hall 4303

Speaker: 
Kentaro Sato Department of Mathematics University of Michigan 
Title: 
The strength of extensionality

Abstract: 
The prooftheoretic strength of the axiom of extensionality, as well as those of other settheoretic axioms (e.g., the axiom of regularity, foundation axioms, the axiom of choice, separation axioms), will be investigated, on quite weak settings with and without the axiom of infinity. The tool is mutual interpretability with subsystems of second order arithmetic (in the infinite case) or with twosorted bounded arithmetic (in the noninfinite case). As a result, it will turn out that the axiom of extensionality is relatively stronger than other (weak) axioms and than previously considered. 