Abstract
We introduce the notion of positive local combinatorial dividing-lines in model theory. We show these are equivalently characterized by indecomposable algebraically trivial Fraïssé classes and by complete prime filter classes. We exhibit the relationship between this and collapse-of-indiscernibles dividing-lines. We examine several test cases, including those arising from various classes of hypergraphs.
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Guingona, V., Hill, C.D. On positive local combinatorial dividing-lines in model theory. Arch. Math. Logic 58, 289–323 (2019). https://doi.org/10.1007/s00153-018-0635-2
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DOI: https://doi.org/10.1007/s00153-018-0635-2