论文标题
多维精确类，平滑近似和有界的4型
Multidimensional exact classes, smooth approximation and bounded 4-types
论文作者
论文摘要
与Anscombe，MacPherson，Steinhorn和[1]的现任作者的工作有关，我们研究了多维精确类（$ R $ -MEC）的概念，这是一种特殊的多维渐近类（$ r $ -MAC），具有测量功能，可产生确切的设置的确切尺寸，而不仅仅是近似设置。我们使用有关平滑近似[24]的结果和撒谎的坐标[14]来证明以下结果（定理4.6.4），如MacPherson的猜想：对于任何可数语言$ \ Mathcal {l} $和任何积极的integer $ d $ the类$ \ ntecal $ \ nathcal {c}（c}（c}（ $ \ MATHCAL {L} $ - 具有最多$ D $ 4类型的结构是$ \ Mathcal {L} $中的多项式精确类，其中多项式精确类是具有多项式测量功能的多维精确类。
In connection with the work of Anscombe, Macpherson, Steinhorn and the present author in [1] we investigate the notion of a multidimensional exact class ($R$-mec), a special kind of multidimensional asymptotic class ($R$-mac) with measuring functions that yield the exact sizes of definable sets, not just approximations. We use results about smooth approximation [24] and Lie coordinatisation [14] to prove the following result (Theorem 4.6.4), as conjectured by Macpherson: For any countable language $\mathcal{L}$ and any positive integer $d$ the class $\mathcal{C}(\mathcal{L},d)$ of all finite $\mathcal{L}$-structures with at most $d$ 4-types is a polynomial exact class in $\mathcal{L}$, where a polynomial exact class is a multidimensional exact class with polynomial measuring functions.
