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 notable 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 such situation,
indicating how equational calculus, Birkhoff's variety theorem and
interpolation results should be adjusted for many-sorted algebras.
You are not logged in |
