Primitive recursive ordered fields and some applications

Victor Selivanov (Institute of Informatics Systems, Novosibirsk)

09-Feb-2021, 13:00-14:00 (3 years ago)

Abstract: We establish primitive recursive versions of some known facts about computable ordered fields of reals and the field of computable reals and then apply them to some problems in linear algebra and analysis. In particular, we find a partial primitive recursive analog of Ershov-Madison’s theorem about real closures of computable ordered fields, relate the corresponding fields to the primitive recursive reals, give sufficient conditions for primitive recursive root-finding, computing normal forms of matrices, and computing solution operators of some linear systems of PDE. This is joint work with Svetlana Selivanova.

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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