Boolean Algebra Approximations
نویسندگان
چکیده
Knight and Stob proved that every low4 Boolean algebra is 0-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0-isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0-isomorphic to any computable Boolean algebra. It is worth remarking that, because of the machinery developed, the proof uses at most a 0′′-priority argument. The technique used to construct this Boolean algebra is new and might be useful in other applications, such as to solve the lown Boolean algebra problem either positively or negatively.
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