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Seminar

DDC - Computability Theory: A topological approach to undefinability in algebraic extensions of the rationals November 13, 2020 (09:00 AM PST - 10:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Linda Westrick (Pennsylvania State University)
Description

Hilbert’s Tenth Problem was the only decision problem among his twenty-three problems. Precise mathematical theory of (in)computability and its interaction with number theory led to the negative solution of the problem. The seminar will focus on modern topics on computability-theoretic phenomena in number-theoretic and other algebraic and model-theoretic structures.

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

 

Video

A topological approach to undefinability in algebraic extensions of the rationals

Abstract/Media

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

Abstract:

Which algebraic extensions of the rationals (AERs) have existentially or universally definable algebraic integers?  Equipping the set of AERs with a natural topology, we show that only a meager subset have this property.  An important tool is a new normal form theorem for existential definitions in AERs.  As a corollary we construct countably many distinct computable AERs whose algebraic integers are neither existentially nor universally definable.  Joint work with Kirsten Eisentraeger, Russell Miller, and Caleb Springer.   This talk will be a more technically detailed presentation of the work described by Springer in his 10/20 talk in the DDC Junior Seminar.

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A topological approach to undefinability in algebraic extensions of the rationals

H.264 Video 25187_28685_8630_A_Topological_Approach_to_Undefinability_in_Algebraic_Extensions_of_the_Rationals_1.mp4