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Definability, Automorphisms, and Dynamic Properties of Computably Enumerable Sets

Leo Harrington and Robert I. Soare
The Bulletin of Symbolic Logic
Vol. 2, No. 2 (Jun., 1996), pp. 199-213
DOI: 10.2307/421110
Stable URL: http://www.jstor.org/stable/421110
Page Count: 15
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Definability, Automorphisms, and Dynamic Properties of Computably Enumerable Sets
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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).

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