Cancellation Meadows: a Generic Basis Theorem and Some Applications

Abstract

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.

24 pages, 6 tables; Inge Bethke is added as an extra author; new title (previous title: A Generic Basis Theorem for Cancellation Meadows)

References in corpus (3)

• The structure of finite meadows
• Differential Meadows
• Square root meadows

Cited by in corpus (13)

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• Square root meadows
• Probabilistic thread algebra
• Equations for formally real meadows
• Timed tuplix calculus and the Wesseling and van den Bergh equation
• Straight-line instruction sequence completeness for total calculation on cancellation meadows