交稠密偏序集完备化中的保交性
Preserving meets in meet-dense poset completions
摘要：
定义P* 为偏序集P的完全格（逆包含序），给出了P* 的子集S允许P到Q的交完备e的充要条件，其中e保持P的向上闭集的下确界当且仅当它在S中.我们证明了，给定S满足这些条件，这些完备化的集合M形成一个加顶的弱下半模格。特别地，当P是有限的时，M是下半模格，并且是自由格的下界同态像。我们提供了一个例子，其中M没有底部元素。
英文摘要：
Defining P* to be the complete lattice of upsets (ordered by reverse inclusion) of a poset P we give necessary and sufficient conditions on a subset S of P* for P to admit a meet-completion e from P to Q where e preserves the infimum of an upwardly closed set from P if and only if it is in S. We show that given S satisfying these conditions the set M of these completions forms a topped weakly lower semimodular lattice. In particular, when P is finite M is a lower semimodular lattice, and a lower bounded homomorphic image of a free lattice. We provide an example where M does not have a bottom element.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
