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Collapse in a Transfinite Hierarchy of Turing Degrees

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thesis
posted on 13.06.2021, 23:17 by Ellen HammattEllen Hammatt

In [2], Downey and Greenberg use the ordinals below ε0 to bound the number of mind-changes of computable approximations. This gives rise to a new transfinite hierarchy in the c.e. degrees; the totally α-c.a. degrees. This hierarchy is significant because it unifies the combinatorics of many constructions as well as giving natural definability results in the c.e. Turing degrees. We study the structure of this hierarchy; in particular we investigate collapse in upper cones. We give a proof in which we build a c.e. set using a strategy tree to show there is no uniform way to find a maximal totally ω^2-c.a. degree above a given totally ω-c.a. degree. Then we discuss extensions of this result.

History

Advisor 1

Greenberg, Noam

Advisor 2

Downey, Rod

Copyright Date

14/06/2021

Date of Award

14/06/2021

Publisher

Victoria University of Wellington - Te Herenga Waka

Rights License

Author Retains Copyright

Degree Discipline

Mathematics

Degree Grantor

Victoria University of Wellington - Te Herenga Waka

Degree Level

Masters

Degree Name

Master of Science

ANZSRC Type Of Activity code

School of Mathematics and Statistics

Victoria University of Wellington Item Type

Awarded Research Masters Thesis

Language

en_NZ

Victoria University of Wellington School

School of Mathematics and Statistics