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Degree Spectra of Relations on Boolean Algebras


We show that every computable relation on a computable Boolean algebra \(\mathfrak{B}\) is either definable by a quantifier-free formula with constants from \(\mathfrak{B}\) (in which case it is obviously intrinsically computable) or has infinite degree spectrum.

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Goncharov, S.S., Downey, R.G. & Hirschfeldt, D.R. Degree Spectra of Relations on Boolean Algebras. Algebra and Logic 42, 105–111 (2003).

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  • computable Boolean algebra
  • computable relation
  • intrinsically computable relation