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Yamaguchi, Jinsei 2014-12-16T06:18:15Z 2014-12-16T06:18:15Z 10000-01-01 1985 1985 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)). Made available in DSpace on 2014-12-16T06:18:15Z (GMT). No. of bitstreams: 1 8600352.pdf: 1463557 bytes, checksum: 2861f60a7881554ed4121c5caddd80e8 (MD5) Previous issue date: 1985 Embargo set by: Seth Robbins for item 71406 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 59 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1985. http://hdl.handle.net/2142/71240 (UMI)AAI8600352 Mathematics Aspects of Large Cardinals (Set Theory, Logic, Measurable, Strongly Compact, Extendible) text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.