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# Decidable prime models

## Research and Teaching Output of the MIT Community

 dc.contributor.advisor Gerald E. Sachs. en_US dc.contributor.author Young, Jessica Millar, 1973- en_US dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US dc.date.accessioned 2005-08-23T21:32:21Z dc.date.available 2005-08-23T21:32:21Z dc.date.copyright 2001 en_US dc.date.issued 2001 en_US dc.identifier.uri http://hdl.handle.net/1721.1/8591 dc.description Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2001. en_US dc.description Includes bibliographical references (leaf 31). en_US dc.description.abstract 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. dc.description.statementofresponsibility by Jessica Millar Young. en_US dc.format.extent 31 leaves en_US dc.format.extent 2928275 bytes dc.format.extent 2928034 bytes dc.format.mimetype application/pdf dc.format.mimetype application/pdf dc.language.iso eng en_US dc.publisher Massachusetts Institute of Technology en_US dc.rights 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. en_US dc.rights.uri http://dspace.mit.edu/handle/1721.1/7582 dc.subject Mathematics. en_US dc.title Decidable prime models en_US dc.type Thesis en_US dc.description.degree Ph.D. en_US dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US dc.identifier.oclc 49279996 en_US
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