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On analyzability in the forking topology for simple theories

Ziv Shami

Annals of Pure and Applied Logic 142 (1):115-124 (2006)

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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
On the forking topology of a reduct of a simple theory.Ziv Shami - 2020 - Archive for Mathematical Logic 59 (3-4):313-324.details Let T be a simple L-theory and let \ be a reduct of T to a sublanguage \ of L. For variables x, we call an \-invariant set \\) in \ a universal transducer if for every formula \\in L^-\) and every a, $$\begin{aligned} \phi ^-\ L^-\text{-forks } \text{ over }\ \emptyset \ \text{ iff } \Gamma \wedge \phi ^-\ L\text{-forks } \text{ over }\ \emptyset. \end{aligned}$$We show that there is a greatest universal transducer \ and it is type-definable. In (...) Download Export citation Bookmark 1 citation
Continuity of SU-rank in unidimensional supersimple theories.Ziv Shami - 2016 - Archive for Mathematical Logic 55 (5-6):663-675.details In a supersimple unidimensional theory, SU-rank is continuous and D-rank is definable. Download Export citation Bookmark
A note on the non‐forking‐instances topology.Ziv Shami - 2020 - Mathematical Logic Quarterly 66 (3):336-340.details The non‐forking‐instances topology (NFI topology) is a topology on the Stone space of a theory T that depends on a reduct of T. This topology has been used in [6] to describe the set of universal transducers for (invariants sets that translate forking‐open sets in to forking‐open sets in T). In this paper we show that in contrast to the stable case, the NFI topology need not be invariant over parameters in but a weak version of this holds for any (...) Download Export citation Bookmark

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