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The classification of small weakly minimal sets I

Part of the Lecture Notes in Mathematics book series (LNM,volume 1292)

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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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18674-8

  • Online ISBN: 978-3-540-48049-5

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