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dc.contributor.authorSmythe, Iian
dc.date.accessioned2018-04-26T14:17:52Z
dc.date.available2018-04-26T14:17:52Z
dc.date.issued2017-08-30
dc.identifier.otherSmythe_cornellgrad_0058F_10391
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:10391
dc.identifier.otherbibid: 10361636
dc.identifier.urihttps://hdl.handle.net/1813/56959
dc.description.abstractWe study examples of set-theoretic phenomena occurring in infinite-dimensional spaces, motivated by functional analysis. This includes equivalence relations induced by ideals of operators on a Hilbert space, a new "local" Ramsey theory for block sequences in Banach spaces and countable discrete vector spaces, analogues of selective ultrafilters and coideals in these settings, and families of infinite-dimensional subspaces which have pairwise finite-dimensional intersection. We draw analogies to the structure of the infinite subsets of the natural numbers.
dc.language.isoen_US
dc.rightsAttribution 4.0 International*
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/*
dc.subjectMathematics
dc.subjectBanach spaces
dc.subjectfunctional analysis
dc.subjectmathematical logic
dc.subjectRamsey theory
dc.subjectset theory
dc.titleSet theory in infinite-dimensional vector spaces
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.committeeMemberMuscalu, Florin Camil
dc.contributor.committeeMemberShore, Richard A.
dcterms.licensehttps://hdl.handle.net/1813/59810
dc.identifier.doihttps://doi.org/10.7298/X4BK19H2


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