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Seminar

DDC Junior Seminar: A topological approach to undefinability in algebraic extensions of the rationals October 20, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Caleb Springer (Pennsylvania State University)
Description

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

The seminar will feature research talks by the six postdoctoral scholars appointed to the Fall 2020 DDC program, along with talks by students and other pre-tenure researchers associated with this program.  Since seminar attendees will have disparate backgrounds, we plan that these talks will not be too advanced, nor will they assume substantial background knowledge.  Our postdocs include number theorists, model theorists, and computable structure theorists, and talks can be expected to span all of these areas.

 

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:

In this talk, we will show that in "most" algebraic extensions of the rational numbers, the ring of integers is neither existentially nor universally definable. To be more precise, we view the set of algebraic extensions of the rationals as a topological space homeomorphic to Cantor space, and show that the subset of fields with an existentially or universally definable ring of integers is meager in this topology. This work was done in collaboration with Kirsten Eisentraeger, Russell Miller and Linda Westrick.

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A Topological Approach To Undefinability In Algebraic Extensions Of The Rationals

H.264 Video 25155_28653_8583_A_Topological_Approach_to_Undefinability_in_Algebraic_Extensions_of_the_Rationals.mp4