Extending Borel's Conjecture from Measure to Dimension
Theodore Slaman (University of California Berkeley)
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
Series comments: Description: Seminar on all areas of logic
| Organizer: | Wesley Calvert* |
| *contact for this listing |