Standard and choiceless set-theoretic geology

• Date/Time: August 30, 2019 (Friday) / 13:00 - 14:00

• Speaker: Prof. T. Usuba (Waseda Univ.)

• Venue: Rm 205, Science Complex A, Tohoku Univ.

• Abstract: The set-theoretic geology, which was initiated by Fuchs-Hamkins-Reitz, is a study of the global structure of all ground models of the universe. It attempts a study of the nature of the forcing method. In this talk, we present a framework of set-theoretic geology and basic results. Meanwhile, the standard geology is a research on ZFC, so the axiom of choice is assumed. However in the current set theory, the forcing method over choiceless model become a common tool. We also present the set-theoretic geology without the axiom of choice.