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On Kueker Simple Theories

Ziv Shami

Journal of Symbolic Logic 70 (1):216 - 222 (2005)

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On analyzability in the forking topology for simple theories.Ziv Shami - 2006 - Annals of Pure and Applied Logic 142 (1):115-124.details We show that in a simple theory T in which the τf-topologies are closed under projections every type analyzable in a supersimple τf-open set has ordinal SU-rank. In particular, if in addition T is unidimensional, the existence of a supersimple unbounded τf-open set implies T is supersimple. We also introduce the notion of a standard τ-metric and show that for simple theories its completeness is equivalent to the compactness of the τ-topology. Download Export citation Bookmark 4 citations
On uncountable hypersimple unidimensional theories.Ziv Shami - 2014 - Archive for Mathematical Logic 53 (1-2):203-210.details We extend the dichotomy between 1-basedness and supersimplicity proved in Shami :309–332, 2011). The generalization we get is to arbitrary language, with no restrictions on the topology [we do not demand type-definabilty of the open set in the definition of essential 1-basedness from Shami :309–332, 2011)]. We conclude that every hypersimple unidimensional theory that is not s-essentially 1-based by means of the forking topology is supersimple. We also obtain a strong version of the above dichotomy in the case where the (...) language is countable. (shrink) Download Export citation Bookmark 1 citation

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