Higher Hierarchies of Equational Theories Lacking Recursive Uniformity

摘要

Pseudorecursive varieties [12] expose and exploit a lack of recursive uniformity related to the number of variables used in equational logic. This article carries their pattern to higher conventional Turing degrees in several ways. It also introduces a supervening hierarchy in which Turing com-putability is replaced by the putative decidability arising from Tarski's claim that these nonrecursive pseudorecursive equational theories are nevertheless decidable. This in turn extends the vista of hypercomputation.