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arXiv · 1507.00548

A negative result on algebraic specifications of the meadow of rational numbers

Jan A. Bergstra·Inge Bethke
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Abstract

$\mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the field of the rational numbers where the multiplicative inverse operation is made total by imposing $0^{-1}=0$. In this note, we prove that $\mathbb{Q}_0$ cannot be specified by the usual axioms for meadows augmented by a finite set of axioms of the form $(1+ \cdots +1+x^2)\cdot (1+ \cdots +1 +x^2)^{-1}=1$.

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Jan A. Bergstra, Inge Bethke. 2015-07-02. A negative result on algebraic specifications of the meadow of rational numbers. https://arxiv.org/abs/1507.00548

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