The geometry of weakly minimal types
1985; Cambridge University Press; Volume: 50; Issue: 4 Linguagem: Inglês
10.2307/2273989
ISSN1943-5886
Autores Tópico(s)Advanced Operator Algebra Research
ResumoAbstract Let T be superstable. We say a type p is weakly minimal if R ( p, L , ∞) = 1. Let M ⊨ T be uncountable and saturated, H = p ( M ). We say D ⊂ H is locally modular if for all X, Y ⊂ D with X = acl( X ) ∩ D, Y = acl( Y ) ∩ D and X ∩ Y ≠ ∅, Theorem 1. Let p ∈ S(A) be weakly minimal and D the realizations of stp( a/A) for some a realizing p. Then D is locally modular or p has Morley rank 1. Theorem 2. Let H, G be definable over some finite A, weakly minimal, locally modular and nonorthogonal. Then for all a ∈ H ∖acl( A ), b ∈ G ∖acl( A ) there are a ′ ∈ H , b ′ ∈ G such that a′ ∈ acl( abb ′ A )∖acl( aA). Similarly when H and G are the realizations of complete types or strong types over A .
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