Let T be superstable. We say a type p is weakly minimal if R(p, L, ∞) = 1. Let $M \models T$ be uncountable and saturated, H = p(M). We say $D \subset H$ is locally modular if for all $X, Y \subset D$ with $X = \operatorname{acl}(X) \cap D, Y = \operatorname{acl}(Y) \cap D$ and $X \cap Y \neq \varnothing$ , dim(X ∪ Y) + dim(X ∩ Y) = dim(X) + dim(Y). Theorem 1. Let p ∈ S(A) be weakly (...) minimal and D the realizations of $\operatorname{stp}(a/A)$ 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 $a \in H\backslash\operatorname{acl}(A), b \in G\operatorname{acl}(A)$ there are a' ∈ H, b' ∈ G such that $a' \in \operatorname{acl}(abb' A)\backslash\operatorname{acl}(aA)$ . Similarly when H and G are the realizations of complete types or strong types over A. (shrink)

Suppose $D \subset M$ is a strongly minimal set definable in M with parameters from C. We say D is locally modular if for all $X, Y \subset D$ , with $X = \operatorname{acl}(X \cup C) \cap D, Y = \operatorname{acl}(Y \cup C) \cap D$ and $X \cap Y \neq \varnothing$ , dim(X ∪ Y) + dim(X ∩ Y) = dim(X) + dim(Y). We prove the following theorems. Theorem 1. Suppose M is stable and $D \subset M$ is strongly minimal. (...) If D is not locally modular then in M eq there is a definable pseudoplane. (For a discussion of M eq see [M, § A].) This is the main part of Theorem 1 of [Z2] and the trichotomy theorem of [Z3]. Theorem 2. Suppose M is stable and $D, D' \subset M$ are strongly minimal and nonorthogonal. Then D is locally modular if and only if D' is locally modular. (shrink)