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|Title:||Aspects of Large Cardinals (Set Theory, Logic, Measurable, Strongly Compact, Extendible)|
|Department / Program:||Mathematics|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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)).
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985.
|Date Available in IDEALS:||2014-12-16|