  Let Q_0 denote the rational numbers expanded to a "meadow", that is, after
taking its zero-totalized form (0^{-1}=0) as the preferred interpretation. In
this paper we consider "cancellation meadows", i.e., meadows without proper
zero divisors, such as $Q_0$ and prove a generic completeness result. We apply
this result to cancellation meadows expanded with differentiation operators,
the sign function, and with floor, ceiling and a signed variant of the square
root, respectively. We give an equational axiomatization of these operators and
thus obtain a finite basis for various expanded cancellation meadows.

Rings and Algebras;Logic in Computer Science