The classification of small weakly minimal sets I

Abstract

Let T be a weakly minimal theory with fewer than Open image in new window 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.