On Beta-Shifts Having Arithmetical Languages
نویسنده
چکیده
Let β be a real number with 1 < β < 2. We prove that the language of the β-shift is ∆n iff β is a ∆n-real. The special case where n is 1 is the independently interesting result that the language of the β-shift is decidable iff β is a computable real. The “if” part of the proof is non-constructive; we show that for Walters’ version of the β-shift, no constructive proof exists.
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