Decidable prime models
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/8591 |
| _version_ | 1811097964787007488 |
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| author | Young, Jessica Millar, 1973- |
| author2 | Gerald E. Sachs. |
| author_facet | Gerald E. Sachs. Young, Jessica Millar, 1973- |
| author_sort | Young, Jessica Millar, 1973- |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. |
| first_indexed | 2024-09-23T17:07:47Z |
| format | Thesis |
| id | mit-1721.1/8591 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T17:07:47Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/85912019-04-10T21:27:16Z Decidable prime models Young, Jessica Millar, 1973- Gerald E. Sachs. 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, 2001. Includes bibliographical references (leaf 31). A set S of types over a theory T is strongly free if for all subsets X [strict subset] S, there is a countable model of T which realizes X and omits S\X. Throughout, all theories are assumed complete and consistent unless otherwise stated. Theorem 1 If all strongly free sets of types over a recursive theory T are finite, then T has a decidable prime model. Definition 2 A model is decidable if it is isomorphic to a model whose elementary diagram is recursive (technically speaking, this just means the model has a decidable presentation. Throughout this paper, however, we will just say the model is decidable} A classical result in model theory is that any theory with less than 2No many countable models must have a prime model. Our theorem gives an effective extension of this result: Corollary 3 If a countable theory T has less than 2No many countable models, then there is a prime model of T decidable in T. by Jessica Millar Young. Ph.D. 2005-08-23T21:32:21Z 2005-08-23T21:32:21Z 2001 2001 Thesis http://hdl.handle.net/1721.1/8591 49279996 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 31 leaves 2928275 bytes 2928034 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mathematics. Young, Jessica Millar, 1973- Decidable prime models |
| title | Decidable prime models |
| title_full | Decidable prime models |
| title_fullStr | Decidable prime models |
| title_full_unstemmed | Decidable prime models |
| title_short | Decidable prime models |
| title_sort | decidable prime models |
| topic | Mathematics. |
| url | http://hdl.handle.net/1721.1/8591 |
| work_keys_str_mv | AT youngjessicamillar1973 decidableprimemodels |