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Mathematics Colloquium
Logic, Degrees, And Definability
Mariya Soskova (University Of Wisconsin--Madison)

Thursday, February 25, 2021
3:30pm – 4:30pm

Storrs Campus
Online

In this talk I will present my take on one line of research in Computability Theory that studies logical properties of degree structures. There are different ways in which we can compare the algorithmic complexity between countable mathematical objects. A set A of natural numbers is Turing reducible to a set B if there is an algorithm to determine membership in A using B as data. A set A is enumeration reducible to B if there is an algorithm to list the members of A using any listing of B as data. Each reducibility gives rise to a degree structure: a partial order in which we identify sets that have equal algorithmic complexity. The Turing degrees and the enumeration degrees are closely related: the Turing degrees have an isomorphic copy inside the enumeration degrees, which we call the total degrees. We study these structures from three interrelated aspects: how complicated is the set of true algebraic statements is each partial order; what relations have structurally definable presentations; what does the automorphism group for each partial order look like?

Contact:

Kyu-Hwan Lee

Mathematics Colloquium (primary), College of Liberal Arts and Sciences, UConn Master Calendar

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