{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/22201"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/22201","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"The power function","abstract":"The axioms of ZFC provide very little information about the possible values of the power function (i.e. the map K---->2ᴷ). In this dissertation, we examine various theorems concerning the behaviour of the power function inside the formal system ZFC , and we :;hall be p:trticul:trly interested in results which provide eonstraints on the possible values of the power function. Thus most of the results presented here will be consistency results. A theorem of Easton (Theorem 2.3.1) shows that, when restricted to regular cardinals, the power function may take on any reasonable value, and thus a considerable part of this thesis is concerned with the power function on singular cardinals. We also examine the influence of various strong axioms of infinity, and their generalization to smaller cardinals, on the possible behaviour of the power function.","abstract_html":"The axioms of ZFC provide very little information about the possible values of the power function (i.e. the map K---->2ᴷ). In this dissertation, we examine various theorems concerning the behaviour of the power function inside the formal system ZFC , and we :;hall be p:trticul:trly interested in results which provide eonstraints on the possible values of the power function. Thus most of the results presented here will be consistency results. A theorem of Easton (Theorem 2.3.1) shows that, when restricted to regular cardinals, the power function may take on any reasonable value, and thus a considerable part of this thesis is concerned with the power function on singular cardinals. We also examine the influence of various strong axioms of infinity, and their generalization to smaller cardinals, on the possible behaviour of the power function.","abstract_has_math":false,"creators":["Ouwehand, Peter"],"institution":"Department of Mathematics and Applied Mathematics","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Rose, Henry"],"committee_chairs":[],"committee_members":[],"year":1993,"date_issued":"1993","date_published":"1993","updated_at":"2026-07-22T22:23:36Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/22201","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Rose, Henry"]},{"key":"dc:creator","label":"Author","values":["Ouwehand, Peter"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2016-10-19T13:36:29Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2016-10-19T13:36:29Z"]},{"key":"dc:date.issued","label":"Date","values":["1993"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Applied Mathematics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/22201"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The axioms of ZFC provide very little information about the possible values of the power function (i.e. the map K---->2ᴷ). In this dissertation, we examine various theorems concerning the behaviour of the power function inside the formal system ZFC , and we :;hall be p:trticul:trly interested in results which provide eonstraints on the possible values of the power function. Thus most of the results presented here will be consistency results. A theorem of Easton (Theorem 2.3.1) shows that, when restricted to regular cardinals, the power function may take on any reasonable value, and thus a considerable part of this thesis is concerned with the power function on singular cardinals. We also examine the influence of various strong axioms of infinity, and their generalization to smaller cardinals, on the possible behaviour of the power function."]},{"key":"dc:title","label":"Title","values":["The power function"]}]}],"canonical_facts":{"dc:contributor.advisor":["Rose, Henry"],"dc:creator":["Ouwehand, Peter"],"dc:date.accessioned":["2016-10-19T13:36:29Z"],"dc:date.available":["2016-10-19T13:36:29Z"],"dc:date.issued":["1993"],"dc:description.abstract":["The axioms of ZFC provide very little information about the possible values of the power function (i.e. the map K---->2ᴷ). In this dissertation, we examine various theorems concerning the behaviour of the power function inside the formal system ZFC , and we :;hall be p:trticul:trly interested in results which provide eonstraints on the possible values of the power function. Thus most of the results presented here will be consistency results. A theorem of Easton (Theorem 2.3.1) shows that, when restricted to regular cardinals, the power function may take on any reasonable value, and thus a considerable part of this thesis is concerned with the power function on singular cardinals. We also examine the influence of various strong axioms of infinity, and their generalization to smaller cardinals, on the possible behaviour of the power function."],"dc:identifier.uri":["http://hdl.handle.net/11427/22201"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Mathematics and Applied Mathematics"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["The power function"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:36Z"}