Kobe Colloquium on Logic, Statistics and Informatics 

以下の要領でコロキウムを開催します。

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.