Recursive inseparability of the sets of identically valid and finitely refutable formulas of some elementary theories of varieties (Q1586995)

The author establishes a correspondence between ternary rings with unit and 2-nilpotent commutative loops in some finitely axiomatizable class. This correspondence makes it possible to obtain the following main results: 1. The sets of identically true and finitary refutable formulas on every nonassociative variety of commutative Moufang loops are recursively inseparable. 2. The theory of a variety of commutative Moufang loops is decidable if and only if the variety is a variety of Abelian groups. 3. The sets of identically true and finitary refutable formulas on the class of all medially 2-nilpotent Steiner distributive quasigroups as well as on every nonmedial variety of distributive quasigroups (CH-quasigroups) are recursively inseparable.