Characterizations of several Maltsev conditions

Tame congruence theory identifies six Maltsev conditions associated with locally finite varieties omitting certain types of local behaviour. Extending a result of Siggers, we show that of these six Maltsev conditions only two of them are equivalent to strong Maltsev conditions for locally finite varieties. Besides omitting the unary type, the only other of these conditions that is strong is that of omitting the unary and affine types.We also provide novel presentations of some of the above Maltsev conditions.