Set theory in infinite-dimensional vector spaces
dc.contributor.author | Smythe, Iian | |
dc.contributor.chair | Moore, Justin Tatch | |
dc.contributor.committeeMember | Muscalu, Florin Camil | |
dc.contributor.committeeMember | Shore, Richard A. | |
dc.date.accessioned | 2018-04-26T14:17:52Z | |
dc.date.available | 2018-04-26T14:17:52Z | |
dc.date.issued | 2017-08-30 | |
dc.description.abstract | We 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.identifier.doi | https://doi.org/10.7298/X4BK19H2 | |
dc.identifier.other | Smythe_cornellgrad_0058F_10391 | |
dc.identifier.other | http://dissertations.umi.com/cornellgrad:10391 | |
dc.identifier.other | bibid: 10361636 | |
dc.identifier.uri | https://hdl.handle.net/1813/56959 | |
dc.language.iso | en_US | |
dc.rights | Attribution 4.0 International | * |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | * |
dc.subject | Mathematics | |
dc.subject | Banach spaces | |
dc.subject | functional analysis | |
dc.subject | mathematical logic | |
dc.subject | Ramsey theory | |
dc.subject | set theory | |
dc.title | Set theory in infinite-dimensional vector spaces | |
dc.type | dissertation or thesis | |
dcterms.license | https://hdl.handle.net/1813/59810 | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Cornell University | |
thesis.degree.level | Doctor of Philosophy | |
thesis.degree.name | Ph. D., Mathematics |
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