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CIE
2005
Springer

On a Question of Sacks - A Partial Solution on the Positive Side

14 years 5 months ago
On a Question of Sacks - A Partial Solution on the Positive Side
Let us say that a c.e. operator E is degree invariant on any given Turing degree a if X, Y ∈ a → E(X) ≡T E(Y ). In [4] we construct a c.e. operator E such that ∀X[X <T E(X) <T X ]. While we are unable to produce degree invariance everywhere, we are able to ensure that for every degree a there exists b such that a ∨ 0 = b ∨ 0 and E is degree invariant on b. What appears here is an abbreviated version of the material from that paper, stopping short of most technical details.
Andrew E. M. Lewis
Added 26 Jun 2010
Updated 26 Jun 2010
Type Conference
Year 2005
Where CIE
Authors Andrew E. M. Lewis
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