论文标题
多重题专业半层次
Multi-argument specialization semilattices
论文作者
论文摘要
如果$ x $是封闭式$ k $的关闭空间，我们将考虑具有进一步关系$ x \ sqsubseteq y_1，y_2，y_2，\ dots，y_n $（y_n $ nivtion $ n+n+1 $ -1 $ n是$ n \ geq 1 $）的$ xsubseteq y_1，y_2，y_2，dots $ quq 1 $ qyq 1 $ qyq 1 $ qyq 1 $ queq 1， ky_2 \ cup \ dots \ cup ky_n $。 我们为这样的“多重题材专业化半纹身”提出了公理，并表明该公理列表是子结构的完整列表，即，满足公理的每个模型都可以嵌入到某种结构中，该结构由某些闭合空间源自上一句话。我们还提供了一个多拨件专业化半静脉内（还原）闭合半静脉的典型嵌入。
If $X$ is a closure space with closure $K$, we consider the semilattice $(\mathcal P(X), \cup)$ endowed with further relations $ x \sqsubseteq y_1, y_2, \dots, y_n$ (a distinct $n+1$-ary relation for each $n \geq 1$), whose interpretation is $x \subseteq Ky_1 \cup Ky_2 \cup \dots \cup Ky_n $. We present axioms for such "multi-argument specialization semilattices" and show that this list of axioms is complete for substructures, namely, every model satisfying the axioms can be embedded into some structure originated by some closure space as in the previous sentence. We also provide a canonical embedding of a multi-argument specialization semilattice into (the reduct of) some closure semilattice.
