On the Triple Jump of the Set of Atoms of a Boolean Algebra
نویسنده
چکیده
We prove the following result about the degree spectrum of the atom relation on a computable Boolean algebra. Let C be a computable Boolean algebra with infinitely many atoms and a be the Turing degree of the atom relation of C. If d is a c.e. degree such that a′′′ ≤T d′′′, then there is a computable copy of C where the atom relation has degree d. In particular, for every high3 c.e. degree d, any computable Boolean algebra with infinitely many atoms has a computable copy where the atom relation has degree d.
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