On positive local combinatorial dividing-lines in model theory

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Archive for Mathematical Logic 58 (3-4):289-323 (2019)
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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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10.1007/s00153-018-0635-2

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Citations of this work

Ranks based on strong amalgamation Fraïssé classes.Vincent Guingona & Miriam Parnes - 2023 - Archive for Mathematical Logic 62 (7):889-929.
Products of Classes of Finite Structures.Vince Guingona, Miriam Parnes & Lynn Scow - 2023 - Notre Dame Journal of Formal Logic 64 (4):441-469.

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On $n$ -Dependence.Artem Chernikov, Daniel Palacin & Kota Takeuchi - 2019 - Notre Dame Journal of Formal Logic 60 (2):195-214.

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