L^k-经典化的几何I：来自有效可构造性的Rosiness
The Geometry of L^k-Canonization I: Rosiness from Efficient Constructibility
摘要：
我们证明了对于有限结构的$k$ -变量理论$T$（满足一定的合并条件），如果$T$的有限模型可以以某种“有效”的方式从$T$模型的有限{ \em子集}的图中恢复，那么$T$是玫瑰色的--事实上，$T$的某种自然$\aleph_0$ -范畴完备$T^{\lim}$是有限$U^\thorn$ -秩的超级玫瑰色的.在附录中，我们还表明，任何$k$ -变量理论$T$的有限结构的强$L^k$ -规范化问题是有效的解决方案有必要的合并属性，以采取适当的redut。
英文摘要：
We demonstrate that for the $k$-variable theory $T$ of a finite structure (satisfying certain amalgamation conditions), if finite models of $T$ can be recovered from diagrams of finite {\em subsets} of model of $T$ in a certain "efficient" way, then $T$ is rosy -- in fact, a certain natural $\aleph_0$-categorical completion $T^{\lim}$ of $T$ is super-rosy of finite $U^\thorn$-rank. In an appendix, we also show that any $k$-variable theory $T$ of a finite structure for which the Strong $L^k$-Canonization Problem is efficient soluble has the necessary amalgamation properties up to taking an appropriate reduct.
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