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MR1802016 (2001m:03085) 03D35 (11U05)
Pheidas, Thanases An effort to prove that the existential theory of $Q$ is undecidable. Hilbert's tenth problem: relations with arithmetic and algebraic geometry (Ghent, 1999), 237--252, Contemp. Math., 270, Amer. Math. Soc., Providence, RI, 2000.
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