It has been a common belief that the standard results of universal algebra as developed since the work of Birkhoff and others in the thirties carry over without much change to the framework of many-sorted algebras. Perhaps the only exception widely noticed by the community is the care needed in the treatment of many-sorted equational logic. However, while the standard results remain valid in essence in the many-sorted frameworks, some nuances and technicalities require considerably more care in formulation and proof of the results. We give some examples of this, indicating how equational calculus, Birkhoff’s variety theorem and interpolation results should be adjusted for many-sorted algebras.
['Andrzej Tarlecki']
Some Nuances of Many-sorted Universal Algebra: A Review