Punctual categoricity and degrees of punctual categoricity for finitely generated structures.

Iskander Kalimullin (Kazan (Volga Region) Federal University)

23-Mar-2021, 14:00-15:00 (3 years ago)

Abstract: A punctual algebraic structure A (i.e., primitive recursive structure on the universe $\omega$) is punctually categorical if for every its punctual copy B there is an isomorphism from A onto B which is primitive recursive together with the inverse. We note that there is an unexpected dichotomy for this notion: every punctually categorical structure is either finitely generated, or locally finite. This dichotomy also holds for the structures which have a degree of punctual categoricity. For the finitely generated structures we can describe the possible degrees of punctual categoricity. We have some partial results relating degrees of punctual categoricity of locally finite structures. The results obtained jointly with Alexander Melnikov.

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
*contact for this listing

Export talk to