Nikolai Bazhenov (Sobolev Institute of Mathematics)

June 9, 2020 @ 4:00 am – 5:00 am

Title: Rogers semilattices in the analytical hierarchy
by Nikolai Bazhenov (Sobolev Institute of Mathematics) as part of Computability theory and applications

For a countable set S, a numbering of S is a surjective map from ω onto S. A numbering ν is reducible to a numbering μ if there is a computable function f such that ν(x) = μ f(x) for all indices x. The notion of reducibility between numberings gives rise to a class of upper semilattices, which are usually called Rogers semilattices. We discuss recent results on Rogers semilattices induced by numberings in the analytical hierarchy. Special attention is given to the first-order properties of Rogers semilattices. The talk is based on joint works with Manat Mustafa, Sergei Ospichev, and Mars Yamaleev.