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Higher Hierarchies of Equational Theories Lacking Recursive Uniformity
Benjamin Wells

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 computability 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.

Keywords: Pseudorecursive varieties, equational logic, decidable theories, computability, hypercomputation.

MR Classification. Primary: 03D35. Secondary: 03D15, 68Q05, 68Q10, 68Q15.

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