2024/07/21 by Hieronymi, Philipp, Manthe, Sven, Schulz, Chris
#FOS: Computer and information sciences #FOS: Mathematics #Logic (math.LO) #Logic in Computer Science (cs.LO)
paper · doi:10.48550/arxiv.2407.15118
Let α,β∈ ℝ>0 be such that α,β are quadratic and ℚ(α)≠ ℚ(β). Then every subset of ℝn definable in both (ℝ,<,+,ℤ,x↦ αx) and (ℝ,<,+,ℤ,x↦ βx) 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.