The rankable and the compressible sets have been studied for more than a quarter of a century. We ask whether these classes are closed under the most important boolean and other operations. We study this question for both polynomial-time and recursion-theoretic compression and ranking, and for almost every case arrive at a Closed, a Not-Closed, or a Closed-Iff-Well-Known-Complexity-Classes-Collapse result. Although compression and ranking classes are capturing something quite natural about the structure of sets, it turns out that these classes are quite fragile with respect to closure properties, and many fail to possess even the most basic of closure properties. For example, we show that with respect to the join (aka disjoint union) operation: the P-rankable sets are not closed, whether the semistrongly P-rankable sets are closed is closely linked to whether $\mathrm{P}=\mathrm{UP}\cap \mathrm{coUP}$, and the strongly P-rankable sets are closed.

可排名集和可压缩集已经研究了四分之一世纪以上。我们问这些类是否在最重要的布尔值和其他操作下被关闭。我们针对多项式时间和递归理论的压缩和排序研究了这个问题，并且几乎在每种情况下都得出了封闭，未封闭或封闭-Iff-Well-已知复杂性-类-折叠的结果。尽管压缩和排序类捕获了关于集合结构的一些自然现象，但事实证明，这些类在闭包属性方面相当脆弱，而且许多类甚至都没有最基本的闭包属性。例如，我们证明了关于联接（又称不相交联合）的操作：P等级集不封闭，$\mathrm{P}=\mathrm{向上}\cap \mathrm{政变}$，并且强P级排名集将关闭。