Applying, extending, and specializing pseudorecursiveness Original Research Article

Pseudorecursive varieties (Inter. J. Algebra Comput. 6 (1996) 457) exhibit a lack of recursive uniformity, expressing the failure of universal and existential quantifiers to reverse. Several examples are given of personal encounters with infeasible or errant quantifier reversal. Results strengthening and applying pseudorecursiveness are followed by the study of a property of spectra that is not uniform. These foreshadow an abstraction of this notion and its integration with the algebraic and computational studies—steps that may eventually help explicate Tarskiʹs claim that recursively enumerable, nonrecursive but pseudorecursive equational theories are nonetheless decidable.