Toshimichi Usuba

J-GLOBAL         Last updated: Aug 21, 2018 at 10:30
Toshimichi Usuba
Waseda University
School of Fundamental Science and Engineering
Job title
Associate Professor
Ph. D.(Nagoya University)


I am working in set theory, especially set theory with large cardinals.

Research Areas


Academic & Professional Experience

Apr 2016
Associate Professor, School of Fundamental Science and Engineering, Waseda University
Apr 2013
Mar 2016
Assistant Professor, Organization of Advanced Science and Technology Core Research Team, Kobe University
Sep 2010
Mar 2013
Designed Assistant Professor, Institute for Advanced Research, Nagoya University
May 2009
Aug 2010
Post-Doc Researcher, Hausdorff Center for Mathematics, University of Bonn
Apr 2008
Mar 2009
Post-Doc Researcher, Graduate School of Science, Tohoku University


Toshimichi Usuba
Archive for Mathematical Logic   1-5   Apr 2018
© 2018 Springer-Verlag GmbH Germany, part of Springer Nature The mantle is the intersection of all ground models of V. We show that if there exists an extendible cardinal then the mantle is the smallest ground model of V.
Toshimichi Usuba
Journal of Mathematical Logic   17    Dec 2017
© 2017 World Scientific Publishing Company. A transitive model M of ZFC is called a ground if the universe V is a set forcing extension of M. We show that the grounds ofV are downward set-directed. Consequently, we establish some fundamental theor...
Toshimichi Usuba
Fundamenta Mathematicae   237 249-260   Jan 2017
© Instytut Matematyczny PAN, 2017. By analyzing Dow's construction, we introduce a general construction of regular Lindelof spaces with points Gδ. Using this construction, we prove the following: Suppose that either (1) there exists a regular Lind...
Toshimichi Usuba
Mathematical Logic Quarterly   62 59-71   Feb 2016
© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. We study the subtlety of a cardinal κ and of kΛ. We show that, under a certain large cardinal assumption, it is consistent that kΛ is subtle for some Λ > κ but κ is not subtle, and the consisten...
Toshimichi Usuba
Journal of the Mathematical Society of Japan   68 1081-1098   Jan 2016
© 2016 The Mathematical Society of Japan. Starting from a model with a weakly compact cardinal, we construct a model in which the weak stationary reflection principle for uω2 holds but the Fodor-type reflection principle for uω2 fails. So the stat...