Almost free algebras have polynomial-time decidable problems for canonical forms, class cardinalities, finiteness checks, and isomorphism, plus quantifier elimination after adding tester predicates via a new approach.
Decidability of term algebras extending partial algebras.Lecture Notes in Computer Science, 3634:292–308, 08 2005
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Almost free algebras: from the word problem to elimination of quantifiers
Almost free algebras have polynomial-time decidable problems for canonical forms, class cardinalities, finiteness checks, and isomorphism, plus quantifier elimination after adding tester predicates via a new approach.