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Definability, Automorphisms, and Dynamic Properties of Computably Enumerable Sets

Published online by Cambridge University Press:  15 January 2014

Leo Harrington  and
Robert I. Soare
Leo Harrington
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720-8204, USA.E-mail:leo@math.berkeley.edu
Robert I. Soare
Affiliation:
Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1546, USA.E-mail:soare@math.uchicago.edu, http://www.cs.uchicago.edu/~soare, Papers posted at, ftp:cs.uchicago.edu/ftp/pub/users/soare
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Abstract

We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of Felix Klein's Erlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and the Martin Invariance Conjecture on their Turing degrees, i.e., their information content with respect to relative computability (Turing reducibility).

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 2 , Issue 2 , June 1996 , pp. 199 - 213
Copyright
Copyright © Association for Symbolic Logic 1986

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References

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