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 Title: Aspects of Large Cardinals (Set Theory, Logic, Measurable, Strongly Compact, Extendible) Author(s): Yamaguchi, Jinsei Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Mathematics Abstract: 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).In Chapter II, we study the fine structure of the extendible hierarchy and obtain a general result concerning the duplication of the least ) (kappa) is < (lamda)-extendible, where (lamda) is the target of (kappa)). Issue Date: 1985 Type: Text Description: 59 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985. URI: http://hdl.handle.net/2142/71240 Other Identifier(s): (UMI)AAI8600352 Date Available in IDEALS: 2014-12-16 Date Deposited: 1985
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