A contrast to the low basis theorem

Annals of Pure and Applied Logic 117 (1-3):203-207 (2002)
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Abstract

We prove the existence of a perfect Π01 set of reals such that the uniform join of any of its infinite subsets is above 0′. We explain a couple of ways in which this demonstrates the optimality of the Low Basis Theorem

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10.1016/s0168-0072(01)00116-6

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