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Preprint Number 2680
2680. Philipp Hieronymi, Sven Manthe, Chris Schulz A Cobham theorem for scalar multiplication E-mail: Submission date: Abstract: Let α, β ∈ ℝ_{>0} be such that α, β are quadratic and ℚ(α) ≠ ℚ(β). Then every subset of ℝ^n definable in both (ℝ,<,+,ℤ,x → α x) and (ℝ, < ,+,ℤ,x → β x) is already definable in (ℝ, < ,+,ℤ). As a consequence we generalize Cobham-Semenov theorems for sets of real numbers to β-numeration systems, where β is a quadratic irrational. Mathematics Subject Classification: Keywords and phrases: |
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