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Recursive inseparability of the sets of identically valid and finitely refutable formulas of some elementary theories of varieties. (English. Russian original) Zbl 0953.03054
Sib. Math. J. 41, No. 3, 577-590 (2000); translation from Sib. Mat. Zh. 41, No. 3, 696-711 (2000).
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.

MSC:
03D35 Undecidability and degrees of sets of sentences
20N05 Loops, quasigroups
08B99 Varieties
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References:
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