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The universality of polynomial time Turing equivalence

Published online by Cambridge University Press:  13 July 2016

ANDREW MARKS
ANDREW MARKS*
Affiliation:
University of California, Los Angeles, California, U.S.A. Email: [email protected]
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Abstract

We show that polynomial time Turing equivalence and a large class of other equivalence relations from computational complexity theory are universal countable Borel equivalence relations. We then discuss ultrafilters on the invariant Borel sets of these equivalence relations which are related to Martin's ultrafilter on the Turing degrees.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Special Issue 3: Mind, Mechanism and Mathematics: Computability Unchained , March 2018 , pp. 448 - 456
Copyright
Copyright © Cambridge University Press 2016 

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