On expansions of

Annals of Pure and Applied Logic 171 (8):102809 (2020)
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Abstract

Call a (strictly increasing) sequence (rn) of natural numbers regular if it satisfies the following condition: rn+1/rn→θ∈R>1∪{∞} and, if θ is algebraic, then (rn) 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,<,R) is NIP whenever R is enumerated by a regular sequence that is ultimately periodic modulo m for all m>1.

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Citations of this work

Expansions of the group of integers by Beatty sequences.Ayhan Günaydın & Melissa Özsahakyan - 2022 - Annals of Pure and Applied Logic 173 (3):103062.

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References found in this work

On Superstable Expansions of Free Abelian Groups.Daniel Palacín & Rizos Sklinos - 2018 - Notre Dame Journal of Formal Logic 59 (2):157-169.
Stable theories with a new predicate.Enrique Casanovas & Martin Ziegler - 2001 - Journal of Symbolic Logic 66 (3):1127-1140.
Model Theory: An Introduction.David Marker - 2003 - Bulletin of Symbolic Logic 9 (3):408-409.

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