dc.contributor.author Lamei Ramandi, Hossein Lamei dc.date.accessioned 2018-10-23T13:23:28Z dc.date.available 2018-10-23T13:23:28Z dc.date.issued 2018-05-30 dc.identifier.other LameiRamandi_cornellgrad_0058F_10845 dc.identifier.other http://dissertations.umi.com/cornellgrad:10845 dc.identifier.other bibid: 10489563 dc.identifier.uri https://hdl.handle.net/1813/59478 dc.description.abstract In 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.iso en_US dc.subject Mathematics dc.title ON THE MINIMALITY OF NON-$\sigma$-SCATTERED ORDERS dc.type dissertation or thesis thesis.degree.discipline Mathematics thesis.degree.grantor Cornell University thesis.degree.level Doctor of Philosophy thesis.degree.name Ph. D., Mathematics dc.contributor.chair Moore, Justin Tatch dc.contributor.committeeMember Shore, Richard A. dc.contributor.committeeMember West, James Edward dcterms.license https://hdl.handle.net/1813/59810 dc.identifier.doi https://doi.org/10.7298/X47H1GV0
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