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Volume 1292 of the series Lecture Notes in Mathematics pp 3271
Date:
The classification of small weakly minimal sets I
 Steven BuechlerAffiliated withDepartment of Mathematics, University of California
Abstract
Let T be a weakly minimal theory with fewer than many countable models. Further suppose that T satisfies (S) for all finite A and weakly minimal p ε S(A), if p is nonisolated then p has finite multiplicity.
We prove a structure theorem for T which implies that T has countably many countable models. This proves Vaught's conjecture (in fact, Martin's conjecture) for a large class of weakly minimal theories.
 Title
 The classification of small weakly minimal sets I
 Book Title
 Classification Theory
 Book Subtitle
 Proceedings of the U.S.Israel Workshop on Model Theory in Mathematical Logic held in Chicago, Dec. 15–19, 1985
 Pages
 pp 3271
 Copyright
 1987
 DOI
 10.1007/BFb0082231
 Print ISBN
 9783540186748
 Online ISBN
 9783540480495
 Series Title
 Lecture Notes in Mathematics
 Series Volume
 1292
 Series ISSN
 00758434
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Steven Buechler ^{(1)}
 Author Affiliations

 1. Department of Mathematics, University of California, 94720, Berkeley, California
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