Chapter

Classification Theory

Volume 1292 of the series Lecture Notes in Mathematics pp 32-71

Date:

The classification of small weakly minimal sets I

  • Steven BuechlerAffiliated withDepartment of Mathematics, University of California

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Abstract

Let T be a weakly minimal theory with fewer than
http://static-content.springer.com/image/chp%3A10.1007%2FBFb0082231/MediaObjects/304_3-540-18674-3_Chapter_3_f1.jpg
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.