8.3 The consistency proof -- 8.4 Applications of the consistency proof -- 8.5 Second-order arithmetic -- Problems -- Chapter 9: Set Theory -- 9.1 Axioms for sets -- 9.2 Development of set theory -- 9.3 Ordinals -- 9.4 Cardinals -- 9.5 Interpretations of set theory -- 9.6 Constructible sets -- 9.7 The axiom of constructibility -- 9.8 Forcing -- 9.9 The independence proofs -- 9.10 Large cardinals -- Problems -- Appendix The Word Problem -- Index.

A constructive proof is given which shows that every nonrecursive r.e. many-one degree is represented by the family of decision problems for partial implicational propositional calculi whose well-formed formulas contain at most two distinct variable symbols.

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. (shrink)