Extension theorems, orbits, and automorphisms of the computably enumerable sets (1992)
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| Venue: | Trans. Amer. Math. Soc. Final version as of |
| Citations: | 4 - 4 self |
BibTeX
@ARTICLE{Cholak92extensiontheorems,,
author = {Peter A. Cholak and Leo and A. Harrington},
title = {Extension theorems, orbits, and automorphisms of the computably enumerable sets},
journal = {Trans. Amer. Math. Soc. Final version as of},
year = {1992},
volume = {8}
}
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Abstract
Abstract. We prove an algebraic extension theorem for the computably enumerable sets, E. Using this extension theorem and other work we then show if A and � A are automorphic via Ψ, then they are automorphic via Λ where Λ ↾ L ∗ (A) =ΨandΛ↾E ∗ (A) is∆0 3. We give an algebraic description of when an arbitrary set �A is in the orbit of a computably enumerable set A. We construct the first example of a definable orbit which is not a ∆0 3 orbit. We conclude with some results which restrict the ways one can increase the complexity of orbits. For example, we show that if A is simple and �A is in the same orbit as A, then they are in the same ∆0 6-orbit and, furthermore, we provide a classification of when two simple sets are in the same orbit. 1.
