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Weakly minimal formulas: a global approach

Ludomir Newelski

Annals of Pure and Applied Logic 46 (1):65-94 (1990)

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The geometry of weakly minimal types.Steven Buechler - 1985 - Journal of Symbolic Logic 50 (4):1044-1053.details 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 (...) Download Export citation Bookmark 14 citations
(1 other version)Ultraproducts which are not saturated.H. Jerome Keisler - 1967 - Journal of Symbolic Logic 32 (1):23-46.details In this paper we continue our study, begun in [5], of the connection between ultraproducts and saturated structures. IfDis an ultrafilter over a setI, andis a structure, the ultrapower ofmoduloDis denoted byD-prod. The ultrapower is important because it is a method of constructing structures which are elementarily equivalent to a given structure. Our ultimate aim is to find out what kinds of structure are ultrapowers of. We made a beginning in [5] by proving that, assuming the generalized continuum hypothesis, for (...) Download Export citation Bookmark 24 citations

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