A Generic Basis Theorem for Cancellation Meadows
نویسندگان
چکیده
Let Q0 denote the rational numbers expanded to a “meadow”, that is, after taking its zero-totalized form (0 = 0) as the preferred interpretation. In this paper we consider “cancellation meadows”, i.e., meadows without proper zero divisors, and prove a representation result and a generic completeness result. We apply these results to cancellation meadows extended with the sign function, and with floor and ceiling, respectively.
منابع مشابه
Cancellation Meadows: A Generic Basis Theorem and Some Applications
Let Q0 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 Q0 and prove a generic completeness result. We apply this result to cancellation meadows expanded with differentiation operators, the sign function...
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