Locally finite varieties. (Q1771891)

The following criterion for a variety \(\mathcal V\) is proved: \(\mathcal V\) is locally finite iff \(\mathcal V\) is generated by a regular locally finite class iff the class \(\mathcal V_{SI}\) is regularly locally finite in the weak sense. If \(\mathcal V\) has a finite signature then \(\mathcal V\) is locally finite iff \(\mathcal V\) is generated by a uniformly locally finite class. Corollary: If a variety \(\mathcal V\) is finitely generated then it is locally finite. A number of interesting examples is included.