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On uncountable hypersimple unidimensional theories

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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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Authors and Affiliations

  1. Ariel University, Ariel, Israel

    Ziv Shami

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  1. Ziv Shami
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Correspondence to Ziv Shami.

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Shami, Z. On uncountable hypersimple unidimensional theories. Arch. Math. Logic 53, 203–210 (2014). https://doi.org/10.1007/s00153-013-0362-7

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  • DOI: https://doi.org/10.1007/s00153-013-0362-7

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