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Seminar

DDC Online Seminar: Effective ultrapowers October 09, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Valentina Harizanov (George Washington University)
Description

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Effective Ultrapowers
Abstract/Media

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract:

Effective ultrapowers of structures are computability-theoretic analogs of ultrapowers. We assume that the structures are computable; that is, they have computable domains and decidable atomic diagrams. The role of an ultrafilter is played by an infinite set of natural numbers that is indecomposable into two infinite parts by computably enumerable (i.e., Diophantine) sets. Such indecomposable sets can even have computably enumerable complements. Effective ultrapower construction allows us to build countable non-standard models with interesting properties. Recent work that focuses on effective ultrapowers of the ordered set of natural numbers is joint with R. Dimitrov, A. Morozov, P. Shafer, A. Soskova and S. Vatev. The lecture will require no background in computability theory.

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Effective Ultrapowers

H.264 Video 25132_28630_8559_Effective_Ultrapowers.mp4
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