David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Journal of Symbolic Logic 39 (3):489-495 (1974)
In this paper we investigate some families of decision problems associated with a restricted class of Post canonical forms, specifically, those defined over one-letter alphabets whose productions have single premises and contain only one variable. For brevity sake, we call any such form an RPCF (Restricted Post Canonical Form). Constructive proofs are given which show, for any prescribed nonrecursive r.e. many-one degree of unsolvability D, the existence of an RPCF whose word problem is of degree D and an RPCF with axiom whose decision problem is also of degree D. Finally, we show that both of these results are best possible in that they do not hold for one-one degrees
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Charles E. Hughes (1975). Sets Derived by Deterministic Systems with Axiom. Mathematical Logic Quarterly 21 (1):71-80.
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