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- W2129683684 abstract "The characteristic sequence of hypergraphs 〈 P n : n < ω 〉 associated to a formula φ ( x ; y ) , introduced in Malliaris (2010) [5] , is defined by P n ( y 1 , … , y n ) = ( ∃ x ) ⋀ i ≤ n φ ( x ; y i ) . We continue the study of characteristic sequences, showing that graph-theoretic techniques, notably Szemerédi’s celebrated regularity lemma, can be naturally applied to the study of model-theoretic complexity via the characteristic sequence. Specifically, we relate classification-theoretic properties of φ and of the P n (considered as formulas) to density between components in Szemerédi-regular decompositions of graphs in the characteristic sequence. In addition, we use Szemerédi regularity to calibrate model-theoretic notions of independence by describing the depth of independence of a constellation of sets and showing that certain failures of depth imply Shelah’s strong order property S O P 3 ; this sheds light on the interplay of independence and order in unstable theories." @default.
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- W2129683684 date "2010-10-01" @default.
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- W2129683684 title "Edge distribution and density in the characteristic sequence" @default.
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- W2129683684 doi "https://doi.org/10.1016/j.apal.2010.06.009" @default.
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