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dc.contributor.authorLamei Ramandi, Hossein Lamei
dc.date.accessioned2018-10-23T13:23:28Z
dc.date.available2018-10-23T13:23:28Z
dc.date.issued2018-05-30
dc.identifier.otherLameiRamandi_cornellgrad_0058F_10845
dc.identifier.otherhttp://dissertations.umi.com/cornellgrad:10845
dc.identifier.otherbibid: 10489563
dc.identifier.urihttps://hdl.handle.net/1813/59478
dc.description.abstractIn this dissertation we study the minimality of non-$\sigma$-scattered orders. While there are insightful theorems, due to Laver, about $\sigma$-scattered orders, we will show the class of non-$\sigma$-scattered orders tend to be more chaotic by a number of consistency results. For instance, we show if there is a supercompact cardinal, there is a forcing extension in which there is no minimal non-$\sigma$-scattered linear order. This shows that Laver's theorem regarding $\sigma$-scattered linear orders is sharp. Our work also includes results concerning trees. For instance, we show it is consistent that there is a Kurepa tree which is minimal with respect to club embeddings. Moreover, we show it is consistent that there is a minimal non-$\sigma$-scattered linear order which does not contain any real or Aronszajn type. Working on these problems resulted in a few byproduct theorems as well.
dc.language.isoen_US
dc.subjectMathematics
dc.titleON THE MINIMALITY OF NON-$\sigma$-SCATTERED ORDERS
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.committeeMemberShore, Richard A.
dc.contributor.committeeMemberWest, James Edward
dcterms.licensehttps://hdl.handle.net/1813/59810
dc.identifier.doihttps://doi.org/10.7298/X47H1GV0


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