Takayuki Kihara: Oracle modalities on the modified realizability topos

Speaker: Takayuki Kihara (Nagoya University)

Abstract: In this talk, we discuss the oracle modalities in the total computable setting. Then, using sheaf subtoposes derived from such oracle modalities, we establish separations between various hierarchies of logical principles, including the hierarchies of the weak law of excluded middle WLEM, the lessor limited principle of omniscience LLPO, and Markov’s principle MP.

This is joint work with A. Kajikawa, M. Kaku and S. Nakata.