A Hierarchy of Computably Enumerable Degrees II

Some Recent Developments and New Directions

Authors

  • Rod Downey Victoria University of Wellington
  • Noam Greenberg Victoria University of Wellington https://orcid.org/0000-0003-2917-3848
  • Ellen Hammatt Victoria University of Wellington

DOI:

https://doi.org/10.53733/133

Keywords:

degrees of unsolvability, reducibilities, hierarchies

Abstract

A transfinite hierarchy of Turing degrees of c.e.\ sets has been used to calibrate the dynamics of families of constructions in computability theory, and yields natural definability results. We review the main results of the area, and discuss splittings of c.e.\ degrees, and finding maximal degrees in upper cones.

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Author Biographies

Rod Downey, Victoria University of Wellington

professor of maths, vuw

Noam Greenberg, Victoria University of Wellington

Professor of Mathematics

Ellen Hammatt, Victoria University of Wellington

PhD student

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Published

19-09-2021

How to Cite

Downey, R., Greenberg, N., & Hammatt, E. (2021). A Hierarchy of Computably Enumerable Degrees II: Some Recent Developments and New Directions. New Zealand Journal of Mathematics, 52, 175–231. https://doi.org/10.53733/133

Issue

Section

Vaughan Jones Memorial Special Issue