论文标题
$ f $ - 自动套装理论的贡献
Contributions to the theory of $F$-automatic sets
论文作者
论文摘要
修复Abelian组$γ$和注射式内态$ f \colonγ\至γ$。贝尔和穆萨（Bell and Moosa）的结果有所改善，在这里为生存集，$ f $ - 自动化和$ f $ -ssparsity提供了新的特征。还研究了这些集合的模型理论状态，最终以$ f $ -sparse套件的组合描述为$（γ， +）$稳定，并证明了任何$ f $ -sparse set的扩展。这些方法还用于显示Prime $ p \ ge 7 $，即通过乘法将$（\ Mathbb {f} _p [t]， +）$扩展，仅限于$ t^\ mathbb {n} $是nip。
Fix an abelian group $Γ$ and an injective endomorphism $F \colon Γ\to Γ$. Improving on the results of Bell and Moosa, new characterizations are here obtained for the existence of spanning sets, $F$-automaticity, and $F$-sparsity. The model theoretic status of these sets is also investigated, culminating with a combinatorial description of the $F$-sparse sets that are stable in $(Γ, +)$, and a proof that the expansion of $(Γ, +)$ by any $F$-sparse set is NIP. These methods are also used to show for prime $p\ge 7$ that the expansion of $(\mathbb{F}_p[t], +)$ by multiplication restricted to $t^\mathbb{N}$ is NIP.
