Improving a bounding result for weakly-scattered theories
Author(s)Goddard, Christina M. (Christina Margaret)
Ranks and Vaught's conjecture
Massachusetts Institute of Technology. Dept. of Mathematics.
Gerald E. Sacks.
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In this thesis, we effectively construct a predecessor function for the type definitions in the raw hierarchy for any weakly-scattered theory. Using this predecessor function, we improve a recent bounding result by Sacks for weakly-scattered theories by removing the assumption of a predecessor function from the k-splitting hypothesis. We begin by giving an introduction to the infinitary logic [...] and admissible sets. We then outline results by Sacks that are important in the construction of the predecessor function. We introduce scattered and weakly-scattered theories and their related hierarchies, and explain how they relate to the well-known Scott hierarchy. Using the raw tree hierarchy, we present Sacks' constructive result called the Effective Recovery Process. Using all of these tools, we provide a proof of the existence of a predecessor function for the type definitions and then use it to improve the bounding result by Sacks.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (p. 45).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology