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Wednesday, February 26, 2025
12:00 PM - 1:00 PM
Online Event

Logic Seminar

Canonicity of the Shift
Zoltán Vidnyánszky, Institute of Mathematics, Eötvös Loránd University,

Please note that the time is PST

The shift graph GS on the infinite subsets of the naturals has been introduced by Kechris-Solecki-Todorcevic, alongside with the graph G0. Since then, it has become an important (and essentially unique) tool to establish complexity results concerning Borel coloring problems.

In this talk, we show that much like G0, this graph is rather canonical. First, surprisingly, every acyclic Borel graph given by a function admits a Borel homomorphism to GS. Second, I will discuss that while a G0-like dichotomy in the Borel context is not possible by complexity results, considering more relaxed versions of coloring could allow for positive results in the case of GS and even general coloring problems. Joint work with Balazs Bursics and Anett Kocsis.

For more information, please contact Math Dept. by phone at 626-395-4335 or by email at kechris@caltech.edu.