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 zerototalized 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2008
 DOI:
 10.48550/arXiv.0803.3969
 arXiv:
 arXiv:0803.3969
 Bibcode:
 2008arXiv0803.3969B
 Keywords:

 Mathematics  Rings and Algebras;
 Computer Science  Logic in Computer Science;
 AC;
 RA
 EPrint:
 24 pages, 6 tables