A cardinality version of biegel's nonspeedup theorem

Journal of Symbolic Logic 54 (3):761-767 (1989)
If S is a finite set, let |S| be the cardinality of S. We show that if $m \in \omega, A \subseteq \omega, B \subseteq \omega$ , and |{i: 1 ≤ i ≤ 2 m & x i ∈ A}| can be computed by an algorithm which, for all x 1 ,...,x 2 m , makes at most m queries to B, then A is recursive in the halting set K. If m = 1, we show that A is recursive
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DOI 10.2307/2274739
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Till Tantau (2005). Weak Cardinality Theorems. Journal of Symbolic Logic 70 (3):861 - 878.

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