MacNeille completions and canonical extensions
MacNeille completions and canonical extensions
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MacNeille 完成和规范扩展
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Y. Venema
中科院分区：
文献类型：
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作者：
M. Gehrke;J. Harding;Y. Venema
设V是各种单调有界格展开，即赋予附加运算的有界格，每个有界格在每个坐标下都是保序或逆序的。我们证明了如果V在MacNeille完备化条件下是闭的，那么它在规范扩张下也是封闭的。作为推论，我们证明了在带有算子的布尔代数的情况下，任何这样的簇V都是由关系结构的初等类生成的。我们的主要技术构造表明，单调有界格展开的正则扩张可以嵌入到原始结构的任何充分饱和的初等扩张的MacNeille完备化中。
Let V be a variety of monotone bounded lattice expansions, that is, bounded lattices endowed with additional operations, each of which is order preserving or reversing in each coordinate. We prove that if V is closed under MacNeille completions, then it is also closed under canonical extensions. As a corollary we show that in the case of Boolean algebras with operators, any such variety V is generated by an elementary class of relational structures. Our main technical construction reveals that the canonical extension of a monotone bounded lattice expansion can be embedded in the MacNeille completion of any sufficiently saturated elementary extension of the original structure.