$\mathbb{Q}\setminus \mathbb{Z}$ is diophantine over $\mathbb{Q}$ with 32 unknowns

Geng-Rui Zhang, Zhi-Wei Sun

In 2016 J. Koenigsmann refined a celebrated theorem of J. Robinson by proving that $\mathbb{Q}\setminus \mathbb{Z}$ is diophantine over $\mathbb{Q}$, i.e., there is a polynomial $P(t,x…