科研之友
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摘要
Knight and Stob proved that every low(4) Boolean algebra is 0((6))-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every low(n) Boolean algebra is 0((n+ 2))-isomorphic to a computable one. We show that this is not true for n = 5: there is a low(5) Boolean algebra that is not 0((7))-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 low(n) Boolean algebra problem either positively or negatively.
- 出版日期2014-10
