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 non-isolated 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.
This paper was written while the author held an NSF Postdoctoral Research Fellowship. Much of the research was done as an Assistant Professor at the University of Wisconsin-Milwaukee.
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© 1987 Springer-Verlag
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Buechler, S. (1987). The classification of small weakly minimal sets I. In: Baldwin, J.T. (eds) Classification Theory. Lecture Notes in Mathematics, vol 1292. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082231
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DOI: https://doi.org/10.1007/BFb0082231
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