Turing incomparability in Scott sets

Kučera, Antonín; Slaman, Theodore

doi:10.1090/S0002-9939-07-08871-5

Turing incomparability in Scott sets
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by Antonín Kučera and Theodore A. Slaman PDF

Proc. Amer. Math. Soc. 135 (2007), 3723-3731 Request permission

Abstract:

For every Scott set $\mathcal F$ and every nonrecursive set $X$ in $\mathcal F$, there is a $Y \in \mathcal F$ such that $X$ and $Y$ are Turing incomparable.

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