Name
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. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1016/j.apal.2020.102809 | Annals of Pure and Applied Logic |
Keywords | DocType | Volume |
03B25,03C10,03C35,03C45 | Journal | 171 |
Issue | ISSN | Citations |
8 | 0168-0072 | 0 |
PageRank | References | Authors |
0.34 | 0 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Quentin Lambotte | 1 | 0 | 0.34 |
| Françoise Point | 2 | 21 | 10.04 |