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- W4297319005 abstract "We continue the study of the theories of Baldwin-Shi hypergraphs from $[5]$. Restricting our attention to when the rank $delta$ is rational valued, we show that each countable model of the theory of a given Baldwin-Shi hypergraph is isomorphic to a generic structure built from some suitable subclass of the original class of finite structures with the inherited notion of strong substructure. We introduce a notion of dimension for a model and show that there is a an elementary chain ${mathfrak{M}_{beta}:beta<omega+1}$ of countable models of the theory of a fixed Baldwin-Shi hypergraph with $mathfrak{M}_{beta}preccurlyeqmathfrak{M}_gamma$ if and only if the dimension of $mathfrak{M}_beta$ is at most the dimension of $mathfrak{M}_gamma$ and that each countable model is isomorphic to some $mathfrak{M}_beta$. We also study the regular types that appear in these theories and show that the dimension of a model is determined by a particular regular type. Further, drawing on the work of Brody and Laskowski, we use these structures to give an example of a pseudofinite, $omega$-stable theory with a non-locally modular regular type, answering a question of Pillay in $[9]$." @default.
- W4297319005 created "2022-09-28" @default.
- W4297319005 creator A5057513042 @default.
- W4297319005 date "2018-04-03" @default.
- W4297319005 modified "2023-09-23" @default.
- W4297319005 title "Countable models of the theories of Baldwin-Shi hypergraphs and their regular types" @default.
- W4297319005 doi "https://doi.org/10.48550/arxiv.1804.00932" @default.
- W4297319005 hasPublicationYear "2018" @default.
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