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Remarks on Tao's algebraic regularity lemma

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arxiv 1310.7538 v1 pith:HWPWSSMV submitted 2013-10-28 math.NT

classification math.NT
keywords lemmaalgebraicregularityelwesgiveholdhrushovskilevel
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We give a stability theoretic proof of the algebraic regularity lemma of Tao, making use of a lemma of Hrushovski. We also point out that the underlying results hold at the level of measurable theories and structures in the sense of Elwes, Macpherson and Steinhorn.

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    Functions built from intersections of set families satisfy a strong hypergraph regularity lemma, and the two known sources of ternary instability both satisfy this regularity, so strong 2-stability cannot be defined b...

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