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Seminar

MT Research Seminar: Tameness and coincidence of dimensions in expansions of the real field April 15, 2014 (03:30 PM PDT - 05:00 PM PDT)
Parent Program: Model Theory, Arithmetic Geometry and Number Theory
Location: MSRI: Simons Auditorium
Speaker(s) Chris Miller (Ohio State University)
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Philipp Hieronymi and I have recently established that if E is a boolean combination of open subsets of real euclidean n-space, and the expansion of the real field by E does not define the set of all integers, then the Lebesgue covering dimension of E is equal to its Assouad dimension (hence also to its Hausdorff and packing dimensions, and also to its upper Minkowski dimension if E is bounded). The proof is too technical to attempt in a seminar talk, but the result is surprisingly easy to prove for the case n=1. Indeed, I will prove the

(possibly) stronger result that all reasonable (in a way that I will make precise) Lipschitz invariant metric dimensions then coincide on E.

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