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Ranks based on strong amalgamation Fraïssé classes

Vincent Guingona & Miriam Parnes

Archive for Mathematical Logic 62 (7):889-929 (2023)

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On $n$ -Dependence.Artem Chernikov, Daniel Palacin & Kota Takeuchi - 2019 - Notre Dame Journal of Formal Logic 60 (2):195-214.details In this article, we develop and clarify some of the basic combinatorial properties of the new notion of n-dependence recently introduced by Shelah. In the same way as dependence of a theory means its inability to encode a bipartite random graph with a definable edge relation, n-dependence corresponds to the inability to encode a random -partite -hypergraph with a definable edge relation. We characterize n-dependence by counting φ-types over finite sets, and in terms of the collapse of random ordered -hypergraph (...) Download Export citation Bookmark 5 citations
On positive local combinatorial dividing-lines in model theory.Vincent Guingona & Cameron Donnay Hill - 2019 - Archive for Mathematical Logic 58 (3-4):289-323.details 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. Download Export citation Bookmark 2 citations
Characterizing model-theoretic dividing lines via collapse of generalized indiscernibles.Vincent Guingona, Cameron Donnay Hill & Lynn Scow - 2017 - Annals of Pure and Applied Logic 168 (5):1091-1111.details Download Export citation Bookmark 6 citations
On a common generalization of Shelah's 2-rank, dp-rank, and o-minimal dimension.Vincent Guingona & Cameron Donnay Hill - 2015 - Annals of Pure and Applied Logic 166 (4):502-525.details Download Export citation Bookmark 4 citations
Indiscernibles, EM-Types, and Ramsey Classes of Trees.Lynn Scow - 2015 - Notre Dame Journal of Formal Logic 56 (3):429-447.details The author has previously shown that for a certain class of structures $\mathcal {I}$, $\mathcal {I}$-indexed indiscernible sets have the modeling property just in case the age of $\mathcal {I}$ is a Ramsey class. We expand this known class of structures from ordered structures in a finite relational language to ordered, locally finite structures which isolate quantifier-free types by way of quantifier-free formulas. This result is applied to give new proofs that certain classes of trees are Ramsey. To aid this (...) Download Export citation Bookmark 9 citations
Book Reviews. [REVIEW]Wilfrid Hodges - 1997 - Studia Logica 64 (1):133-149.details Download Export citation Bookmark 109 citations
Karp complexity and classes with the independence property.M. C. Laskowski & S. Shelah - 2003 - Annals of Pure and Applied Logic 120 (1-3):263-283.details A class K of structures is controlled if for all cardinals λ, the relation of L∞,λ-equivalence partitions K into a set of equivalence classes . We prove that no pseudo-elementary class with the independence property is controlled. By contrast, there is a pseudo-elementary class with the strict order property that is controlled 69–88). Download Export citation Bookmark 6 citations

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