2026-09-28T02:45:56Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/85912022-01-13T07:54:35Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Gerald E. Sachs.
Young, Jessica Millar, 1973-
Massachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2005-08-23T21:32:21Z
2005-08-23T21:32:21Z
2001
2001
http://hdl.handle.net/1721.1/8591
49279996
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.
31 leaves
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2928034 bytes
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Massachusetts Institute of Technology
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http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Decidable prime models
Thesis
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