Classification Theory

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


The classification of small weakly minimal sets I

  • Steven BuechlerAffiliated withDepartment of Mathematics, University of California

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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.