Kobe Colloquium on Logic, Statistics and Informatics

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日時：2013年5月28日（火）13:20-14:50 講演者：Daisuke Ikegami (University of California, Berkeley) 場所：神戸大学自然科学総合研究棟3号館4階421室（プレゼンテーション室）

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題目： Inner models from logics

アブストラクト： The goal of this research is to construct a model of set theory which is "close to" HOD but easier to analyze. The motivation comes from Woodin's HOD Conjecture, which states that HOD is very "close to" V under the presence of a very strong large cardinal (extendible cardinal). HOD Conjecture is closely related to the problem of constructing a canonical extender model with a supercompact cardinal and it has striking applications to the theory of large cardinals without the Axiom of Choice.

To solve HOD Conjecture, one would expect a fine analysis of HOD. The difficulty of the analysis of HOD lies in the fact that HOD is very "non-absolute", e.g., one could force V = HOD with a proper class partial order.

Given that HOD is obtained using full second order logic in the same way as Gödel's constructible universe L via first order logic, in this talk, we use Boolean valued higher order logics to construct inner models of set theory which are more "absolute" than HOD and investigate the properties of the models.

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交通：阪急六甲駅またはJR六甲道駅から神戸市バス36系統「鶴甲団地」 行きに乗車，「神大本部工学部前」停留所下車，徒歩すぐ． http://www.kobe-u.ac.jp/info/access/rokko/rokkodai-dai2.htm

連絡先：ブレンドレ ヨーグ [email protected]