论文标题
通过比蒂序列扩展整数
Expansions of the Group of Integers by Beatty Sequences
论文作者
论文摘要
我们研究模型理论结构$（\ z，+，p_r）$，其中$ r> 1 $是一个不合理的编号，$ p_r $的元素是$ \ floor {nr} $的$ \ floes {nr} $，对于某些$ n \ in \ z \ z \ setMinus \ {0 \} $。我们公理地对此结构进行了证明，并证明了量词消除结果。结果，除非有限，否则我们得到可确定的子集并不稀疏。我们还证明，没有扩展$（\ z，+）$的结构的减少。
We study the model theoretic structure $(\Z,+,P_r)$ where $r>1$ is an irrational number and the elements of $P_r$ are of the form $\floor{nr}$ for some $n\in\Z\setminus\{0\}$. We axiomatize of this structure and prove a quantifier elimination result. As a consequence, we get that definable subsets are not sparse unless they are finite. We also prove that there are no reducts of this structure expanding $(\Z,+)$.
