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Seminar

DDC - Computability Theory: Indestructibility on sets of positive upper density October 22, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Rehana Patel (African Institute for Mathematical Sciences (AIMS))
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

 

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

Abstract:

A structure M is said to be indestructible on a subset of its underlying set if the substructure induced on this subset contains a copy of M.  Recently, W. Brian has shown that almost every Rado graph with underlying set the natural numbers is indestructible on any subset of positive upper density.  In this talk I will consider indestructibility, on all subsets of positive upper density, for arbitrary ultrahomogeneous relational structures on the naturals that are Martin-Löf random for some invariant measure.  This is preliminary work, joint with N. Ackerman and C. Freer.

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