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Elliptic divisibility sequences and undecidable problems about rational points
Julia Robinson has given a first-order definition of the rational integers ℤ in the rational numbers ℚ by a formula (∀∃∀∃) (F = 0) where the ∀-quantifiers run over a total of 8 variables, and where F is a polynomial. This implies that the Σ5-theory of ℚ is undecidable. We …