The classification of small weakly minimal sets I

  • Steven Buechler
Conference paper

DOI: 10.1007/BFb0082231

Volume 1292 of the book series Lecture Notes in Mathematics (LNM)
Cite this paper as:
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

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.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Steven Buechler
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeley