置换、圆柱化和复合下闭运算集的Galois联络
Galois connection for sets of operations closed under permutation, cylindrification and composition
摘要：
我们考虑集合A上的运算集合，这些运算集合在变量的置换、虚变量的加法和组合下是封闭的。我们描述这些闭集的操作和系统之间的伽罗瓦连接点的多重集，我们还描述了封闭的对偶对象的必要和充分的封闭条件。此外，我们证明了相应的闭包系统是不可数的任何A至少有两个元素。
英文摘要：
We consider sets of operations on a set A that are closed under permutation of variables, addition of dummy variables and composition. We describe these closed sets in terms of a Galois connection between operations and systems of pointed multisets, and we also describe the closed sets of the dual objects by means of necessary and sufficient closure conditions. Moreover, we show that the corresponding closure systems are uncountable for every A with at least two elements.
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