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Robinson by proving that $\\mathbb Q\\setminus\\mathbb Z$ is diophantine over $\\mathbb Q$, i.e., there is a polynomial $P(t,x_1,\\ldots,x_{n})\\in\\mathbb Z[t,x_1,\\ldots,x_{n}]$ such that for any rational number $t$ we have $$t\\not\\in\\mathbb Z\\iff \\exists x_1\\cdots\\exists x_{n}[P(t,x_1,\\ldots,x_{n})=0]$$ where variables range over $\\mathbb Q$, equivalently $$t\\in\\mathbb Z\\iff \\forall x_1\\cdots\\forall x_{n}[P(t,x_1,\\ldots,x_{n})\\not=0].$$ In this paper we prove that we may take $n=32$. Combining this with a result of Z.-W. 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