On uncountable hypersimple unidimensional theories |
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Authors: | Ziv Shami |
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Institution: | 1. Ariel University, Ariel, Israel
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Abstract: | We extend the dichotomy between 1-basedness and supersimplicity proved in Shami (J Lond Math Soc 83(2):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 (J Lond Math Soc 83(2):309–332, 2011)]. We conclude that every (possibly uncountable) 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. |
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