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I think a candidate for such a set $\mathbb{B}$, or something very much like it, could be produced by considering an infinite sequence of singleton languages: $L_1=\{w_1\},L_2=\{w_2\},\ldots$ --- where the $w_1\cdot w_2\cdot\ldots$ form an incompressible sequence. You might be able to shave off a bit here or there (this will strongly depend on the encoding --...

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