可表示性的无限层;某些柱形代数比其它的更可表示
An infinite stratum of representability; some cylindric algebras are more representable than others
摘要：
令$2<n<m\leq ω$。设$\CA_n$表示维数为$n$的柱形代数类，$\RCA_n$表示可表示的$\CA_n$类.如果$\Cm\At\A$具有$m$ -平方表示，则我们说$\A\in \RCA_n$可表示到$m$. $m$平方表示是局部相对化表示，其仅在所谓的$m$平方上局部经典。粗略地说，如果我们通过一个可移动的窗口放大到一个$m$正方形表示，就会有一个确定的点，并且取决于$m$，我们将$m$正方形表示误认为是真正的经典表示。当我们缩小时，不可表示的部分会暴露得更多。对于$2<n<m<l\leq ω$，$l$的平方表示是$m$ -平方;反之则不成立。变种$\RCA_n$是与具有$ω$ -平方表示的$\CA_n$一致的限制情况。设$\RCA_n^m$是可表示到$m$的代数类。我们表明，$\RCA_n^{m+1}\subsetneq \bold \RCA_n^m$为$m\geq n+2$。
英文摘要：
Let $2<n<m\leq ω$. Let $\CA_n$ denote the class of cylindric algebras of dimension $n$ and $\RCA_n$ denote the class of representable $\CA_n$s. We say that $\A\in \RCA_n$ is representable up to $m$ if $\Cm\At\A$ has an $m$-square representation. An $m$ square represenation is locally relativized represenation that is classical locally only on so called $m$-squares'. Roughly if we zoom in by a movable window to an $m$ square representation, there will become a point determinded and depending on $m$ where we mistake the $m$ square-representation for a genuine classical one. When we zoom out the non-representable part gets more exposed. For $2<n<m<l\leq ω$, an $l$ square represenation is $m$-square; the converse however is not true. The variety $\RCA_n$ is a limiting case coinciding with $\CA_n$s having $ω$-square representations. Let $\RCA_n^m$ be the class of algebras representable up to $m$. We show that $\RCA_n^{m+1}\subsetneq \bold \RCA_n^m$ for $m\geq n+2$.
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