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Preprint Number 1437
1437. Philipp Hieronymi, Danny Nguyen, Igor Pak Presburger Arithmetic with algebraic scalar multiplications E-mail: Submission date: 9 May 2018 Abstract: We study complexity of integer sentences in S_α=( ℝ , < , + , ℤ , x↦ αx), which is known to be decidable for quadratic α, and undecidable for non-quadratic irrationals. When α is quadratic and the sentence has r alternating quantifier blocks, we prove both lower and upper bounds as towers of height (r-3) and r, respectively. We also show that for α non-quadratic, already r=4 alternating quantifier blocks suffice for undecidability. Mathematics Subject Classification: Keywords and phrases: |
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