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dc.contributor.authorBergfalk, Jeffrey
dc.date.accessioned2018-10-23T13:33:40Z
dc.date.available2020-08-22T06:01:06Z
dc.date.issued2018-08-30
dc.identifier.otherBergfalk_cornellgrad_0058F_10941
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:10941
dc.identifier.otherbibid: 10489672
dc.identifier.urihttps://hdl.handle.net/1813/59576
dc.description.abstractWe describe an organizing framework for the study of infinitary combinatorics. This framework is Cˇech cohomology. It describes ZFC combinatorial principles distinguishing among higher ωn. More precisely, it correlates each ωn with an (n + 1)-dimensional generalization of Todorcevic’s walks technique, and begins to explain that technique’s "unreasonable effectiveness" on ω1. We show in contrast that on higher cardinals κ, the existence of these principles is frequently independent of the ZFC axioms. Finally, we detail implications of these phenomena for the computation of strong homology groups and higher derived limits, deriving independence results in algebraic topology and homological algebra, respectively, in the process.
dc.language.isoen_US
dc.subjectCech cohomology
dc.subjectcoherence
dc.subjectderived limit
dc.subjectomega_n
dc.subjectordinal
dc.subjectwalks
dc.subjectMathematics
dc.subjectLogic
dc.titleDimensions of ordinals: set theory, homology theory, and the first omega alephs
dc.typedissertation or thesis
thesis.degree.disciplineMathematics
thesis.degree.grantorCornell University
thesis.degree.levelDoctor of Philosophy
thesis.degree.namePh. D., Mathematics
dc.contributor.chairMoore, Justin Tatch
dc.contributor.committeeMemberStillman, Michael Eugene
dc.contributor.committeeMemberWest, James Edward
dcterms.licensehttps://hdl.handle.net/1813/59810
dc.identifier.doihttps://doi.org/10.7298/X4W37TKK


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