Maltsev Conditions Research Articles

Subtraces and shadow chains

Given a finite algebra A, such that the variety $ \cal V = ({\bf A})$ omits type 1, it is shown that type 5 will occur in $ \cal V$ only if type 5 already occurs in the free algebra on two generators. The technique generalizes to give the decidability of other typesets, and provides a simpler alternative to what had previously required Maltsev conditions.