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Thesis - Campus Access Only
Master of Science (MS)
The goal of this project is to demonstrate how a version of Jensen's square
principle can be used to produce subsets of aleph_(omega+1) with a wide variety of possible structures. After some preliminaries, the concept of a colored square sequence is introduced. It is shown how to construct a colored square sequence from a given aleph_omega-square sequence and how to force a colored square sequence with the property that the set of all ordinals of fixed cofinality having a given "color"--a natural number assigned to each limit ordinal in a coherent way--is stationary in aleph_(omega+1). Using such a sequence, it is possible to construct, given an arbitrary collection of sets z_n^i with i less than or equal to n, a subset X of aleph_(omega+1) such that each z_n^i occurs stationarily often in X .
Sanders, Robert Joseph, "A Square Sequence for Constructing a Subset of Aleph-(omega+1)" (2014). Master's Theses. 4516.