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$\mathbb{Q}_0$ - the involutive meadow of the rational numbers - is the fieldof the rational numbers where the multiplicative inverse operation is madetotal by imposing $0^{-1}=0$. In this note, we prove that $\mathbb{Q}_0$ cannotbe specified by the usual axioms for meadows augmented by a finite set ofaxioms of the form $(1+ \cdots +1+x^2)\cdot (1+ \cdots +1 +x^2)^{-1}=1$.

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