University of Illinois Urbana-Champaign

Kolmogorov Complexity, Strong Reducibilities, and Computably Enumerable Sets

Ho, Kejia

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https://hdl.handle.net/2142/87001

Description

Title
Kolmogorov Complexity, Strong Reducibilities, and Computably Enumerable Sets
Author(s)
Ho, Kejia
Issue Date
2000
Doctoral Committee Chair(s)
Jockusch, Carl G., Jr.
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Computer Science
Language
eng
Abstract
We also study connections between strong reducibilities and properties of computably enumerable sets such as simplicity. We call a class S of computably enumerable sets bounded if there is an m-incomplete computably enumerable set A such that every set in S is m-reducible to A. For example, we show that the class of effectively simple sets is bounded; but the class of maximal sets is not. Furthermore, the class of computably enumerable sets Turing reducible to a computably enumerable set B is bounded if and only if B is low2. For r = bwtt, tt, wtt, and T, there is a bounded class intersecting every computably enumerable r-degree; for r = c, d and p, no such class exists.
Graduation Semester
2000
Type of Resource
text
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http://hdl.handle.net/2142/87001

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