Aspects of Large Cardinals (Set Theory, Logic, Measurable, Strongly Compact, Extendible)

This paper deals with three subjects in set theory. Chapter I concerns a categorical representation of measurable cardinals. The result answers Girard's presumption "The solution to make the order relation between dilators total will be connected to large cardinal axioms, if it exists" negatively. As a byproduct, we obtain the following interesting result concerning Boolean-valued measurability: ZFC (TURNST) ((FOR ALL)(kappa)) ((kappa) is Boolean-valued measurable whose target cBa is a field of sets (--->) (kappa) is measurable).

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Yamaguchi, Jinsei

• Mathematics

Identifier

(UMI)AAI8600352

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/71240