On expansions of (Z,+,0)

2017/02/15 by Quentin Lambotte, Lambotte, Quentin, Françoise Point +1
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Computability, Logic, AI Algorithms #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1702.04795

Abstract

Call a (strictly increasing) sequence (r_n) of natural numbers regular if it satisfies the following condition: r_n+1/r_n→θ∈ℝ^>1∪\∞\ and, if θ is algebraic, then (r_n) satisfies a linear recurrence relation whose characteristic polynomial is the minimal polynomial of θ. Our main result states that (ℤ,+,0,R) is superstable whenever R is enumerated by a regular sequence. We give two proofs of this result. One relies on a result of E. Casanovas and M. Ziegler and the other on a quantifier elimination result. We also show that (ℤ,+,0,1.

Citations

• Linear Equations in Variables which Lie in a Multiplicative Group

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