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On the Minimality of Non-sigma-Scattered Orders
Başlık:
On the Minimality of Non-sigma-Scattered Orders
Yazar:
Ramandi, Hossein Lamei, author.
ISBN:
9780438027084
Yazar Ek Girişi:
Fiziksel Tanımlama:
1 electronic resource (74 pages)
Genel Not:
Source: Dissertation Abstracts International, Volume: 79-10(E), Section: B.
Advisors: Justin T. Moore Committee members: Richard A. Shore; James E. West.
Özet:
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.
Notlar:
School code: 0058
Konu Başlığı:
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Yer Numarası | Demirbaş Numarası | Shelf Location | Lokasyon / Statüsü / İade Tarihi |
---|---|---|---|
XX(681420.1) | 681420-1001 | Proquest E-Tez Koleksiyonu | Arıyor... |
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