Models of high rank for weakly scattered theories
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2006
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| Online Access: | http://hdl.handle.net/1721.1/34557 |
| _version_ | 1826207034968637440 |
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| author | Chan, Alice Shih Ying |
| author2 | Gerald E. Sacks. |
| author_facet | Gerald E. Sacks. Chan, Alice Shih Ying |
| author_sort | Chan, Alice Shih Ying |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006. |
| first_indexed | 2024-09-23T13:42:28Z |
| format | Thesis |
| id | mit-1721.1/34557 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:42:28Z |
| publishDate | 2006 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/345572019-04-10T22:31:05Z Models of high rank for weakly scattered theories Chan, Alice Shih Ying 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 (leaves 32-33). The Scott rank of a countable structure A, denoted sr(A), was observed by Nadel to be at most wA + 1, where wA4 is the least ordinal not recursive in A. Let T be weakly scattered and L(a,T) be E2-admissible. We give a sufficient condition, the B,-hypothesis, under which T has model A with w4A = a and sr(A) = a + 1. Given the B,-hypothesis, an iterated forcing argument is used to obtain a generic Ta D T such that Th has a model with the desired properties. by Alice Shih Ying Chan. Ph.D. 2006-11-07T12:56:17Z 2006-11-07T12:56:17Z 2006 2006 Thesis http://hdl.handle.net/1721.1/34557 71125510 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 33 leaves 1185111 bytes 1186441 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Chan, Alice Shih Ying Models of high rank for weakly scattered theories |
| title | Models of high rank for weakly scattered theories |
| title_full | Models of high rank for weakly scattered theories |
| title_fullStr | Models of high rank for weakly scattered theories |
| title_full_unstemmed | Models of high rank for weakly scattered theories |
| title_short | Models of high rank for weakly scattered theories |
| title_sort | models of high rank for weakly scattered theories |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/34557 |
| work_keys_str_mv | AT chanaliceshihying modelsofhighrankforweaklyscatteredtheories |