{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71240"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71240","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Aspects of Large Cardinals (Set Theory, Logic, Measurable, Strongly Compact, Extendible)","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).","abstract_html":"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).","abstract_has_math":false,"creators":["Yamaguchi, Jinsei"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T06:18:15Z","date_published":"2014-12-16T06:18:15Z","updated_at":"2026-07-22T22:26:04Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8600352"],"render_values":[{"text":"(UMI)AAI8600352","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71240","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Yamaguchi, Jinsei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T06:18:15Z","10000-01-01","1985"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71240","(UMI)AAI8600352"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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). 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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). 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