Rogers semilattices in the analytical hierarchy

Nikolai Bazhenov (Sobolev Institute of Mathematics)

09-Jun-2020, 14:00-15:00 (4 years ago)

Abstract: 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.

logic

Audience: researchers in the topic


Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.

Organizers: Damir Dzhafarov*, Vasco Brattka*, Ekaterina Fokina*, Ludovic Patey*, Takayuki Kihara, Noam Greenberg, Arno Pauly, Linda Brown Westrick
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