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.
MetadataShow full item record
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. Department of Mathematics
Massachusetts Institute of Technology