2026-09-19T12:34:05Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/345472022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Gerald E. Sacks.
Goddard, Christina M. (Christina Margaret)
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2006-11-07T12:53:42Z
2006-11-07T12:53:42Z
2006
2006
http://hdl.handle.net/1721.1/34547
71015183
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
Includes bibliographical references (p. 45).
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.
by Christina M. Goddard.
Ph.D.
45 p.
1803533 bytes
1805301 bytes
application/pdf
application/pdf
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Improving a bounding result for weakly-scattered theories
Ranks and Vaught's conjecture
Thesis
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