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dc.contributor.advisorBaldwin, John T.en_US
dc.contributor.authorDrueck, Fred R.en_US
dc.date.accessioned2013-06-28T17:46:18Z
dc.date.available2013-06-28T17:46:18Z
dc.date.created2013-05en_US
dc.date.issued2013-06-28
dc.date.submitted2013-05en_US
dc.identifier.urihttp://hdl.handle.net/10027/9996
dc.description.abstractThis dissertation examines three main topics, the topic of defining "superstability" for abstract elementary classes (AECs), uniqueness of limit models, and two cardinal models in abstract elementary classes. In particular we further generalize an analogue of Vaught's theorem which constructs an uncountable two cardinal model starting from the existence of a countable Vaughtian pair in an elementary class to the AEC context originally published by Lessmann, who in turn built upon the work of Grossberg and VanDieren, Shelah, and others. We also give various sufficient conditions on countable models, as well as a condition on models of size kappa that, assuming that a simplified morass,ñ allows us to construct a (kappa^++,kappa)-model. We discuss how this work in AECs to some degree parallels the proof of Jensen's Gap-2 transfer theorem for elementary classes. We also discuss difficulties inherent in proving a true gap-2 transfer theorem for AECs. Additionally, we discuss, progress that has been made toward proving the uniqueness of limit models assuming various "superstability-like" assumptions (much of the work described is due to Shelah, Villaveces, Grossberg, and VanDieren). One small original result is contributed to this discussion.en_US
dc.language.isoenen_US
dc.rightsCopyright 2013 Fred R. Druecken_US
dc.subjectLimit Modelsen_US
dc.subjectSuperlimit Modelsen_US
dc.subjectTwo Cardinal Problemsen_US
dc.subjecttwo cardinal modelsen_US
dc.subjecttwo cardinalen_US
dc.subject2 cardinalen_US
dc.subject2 cardinal problemsen_US
dc.subject2 cardinal modelen_US
dc.subjectgap-2 transferen_US
dc.subjectgap-2en_US
dc.subjectAbstract Elementary Classesen_US
dc.subjectmathematical logicen_US
dc.subjectuniqueness of limit modelsen_US
dc.subjectmorassesen_US
dc.subjectlessmannen_US
dc.titleLimit Models, Superlimit Models, and Two Cardinal Problems in Abstract Elementary Classesen_US
thesis.degree.departmentMathematics, Statistics, and Computer Scienceen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.grantorUniversity of Illinois at Chicagoen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePhD, Doctor of Philosophyen_US
dc.type.genrethesisen_US
dc.contributor.committeeMemberMarker, Daviden_US
dc.contributor.committeeMemberTakloo-Bighash, Raminen_US
dc.contributor.committeeMemberVanDieren, Monicaen_US
dc.contributor.committeeMemberScow, Lynnen_US
dc.type.materialtexten_US


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