Extending Borel's Conjecture from Measure to Dimension

Theodore Slaman (University of California Berkeley)

Thu Jan 23, 19:00-20:00 (2 months ago)

Abstract: We discuss the general formulation of Hausdorff dimension in terms of gauge measures from the meta-mathematical perspective. There is a natural generalization to the context of dimension of Borel's conjecture that only countable sets have strong measure zero. We show that this generalization is consistent with ZFC.

We propose the question "For which ideals I of gauge measures H does there exist a set such that H(A)>0 exactly when H is an element of I?" We settle a question of C. Rogers (1962) to show that the answer to this question depends on the descriptive complexity of A. In particular, the answer for closed sets is different from that for (even low-level) Borel sets.

logic

Audience: researchers in the topic


Online logic seminar

Series comments: Description: Seminar on all areas of logic

Organizer: Wesley Calvert*
*contact for this listing

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