Improving a bounding result for weakly-scattered theories
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2006
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| Online Access: | http://hdl.handle.net/1721.1/34547 |
| _version_ | 1811079198063722496 |
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| author | Goddard, Christina M. (Christina Margaret) |
| author2 | Gerald E. Sacks. |
| author_facet | Gerald E. Sacks. Goddard, Christina M. (Christina Margaret) |
| author_sort | Goddard, Christina M. (Christina Margaret) |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. |
| first_indexed | 2024-09-23T11:11:25Z |
| format | Thesis |
| id | mit-1721.1/34547 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T11:11:25Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/345472019-04-10T22:22:00Z Improving a bounding result for weakly-scattered theories Ranks and Vaught's conjecture Goddard, Christina M. (Christina Margaret) Gerald E. Sacks. Massachusetts Institute of Technology. Dept. of Mathematics. Massachusetts Institute of Technology. Dept. of Mathematics. Mathematics. 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. 2006-11-07T12:53:42Z 2006-11-07T12:53:42Z 2006 2006 Thesis http://hdl.handle.net/1721.1/34547 71015183 eng 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 45 p. 1803533 bytes 1805301 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Goddard, Christina M. (Christina Margaret) Improving a bounding result for weakly-scattered theories |
| title | Improving a bounding result for weakly-scattered theories |
| title_full | Improving a bounding result for weakly-scattered theories |
| title_fullStr | Improving a bounding result for weakly-scattered theories |
| title_full_unstemmed | Improving a bounding result for weakly-scattered theories |
| title_short | Improving a bounding result for weakly-scattered theories |
| title_sort | improving a bounding result for weakly scattered theories |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/34547 |
| work_keys_str_mv | AT goddardchristinamchristinamargaret improvingaboundingresultforweaklyscatteredtheories AT goddardchristinamchristinamargaret ranksandvaughtsconjecture |