Speaker: Cecelia Higgins
University of California - Los Angeles
Will give a Logic Seminar entitled:
Complexity of Borel asymptotic dimension
Abstract: A Borel graph is hyperfinite if it can be written as a countable increasing union of Borel graphs with finite components. It is a major open problem in descriptive set theory to determine the complexity of the set of hyperfinite Borel graphs. In a recent paper, Conley, Jackson, Marks, Seward, and Tucker-Drob introduce the notion of Borel asymptotic dimension, a definable version of Gromov's classical notion of asymptotic dimension, which strengthens hyperfiniteness and implies several nice Borel combinatorial properties. We show that the set of locally finite Borel graphs having finite Borel asymptotic dimension is $\mathbf{\Sigma}^1_2$-
Date: 04-08-2025
Time: 2:00 pm
Location: 125 Hayes-Healy Bldg