A Uniform Approach to Inductive Posets and Inductive Closure
A Uniform Approach to Inductive Posets and Inductive Closure
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DOI：
10.1016/0304-3975(78)90040-3
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发表时间：
1977-09
期刊：
影响因子：
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通讯作者：
J. Wright;E. Wagner;J. Thatcher
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文献类型：
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作者：
J. Wright;E. Wagner;J. Thatcher
当我们用“定向的”、“链的”、“成对相容的”、“单态的”等形容词代替Z的符号时，“如果一个偏序集P有一个由Z紧元组成的集合B，使得P的每一个元素在B中都有一个Z集S，使得P =⨆S，那么它就是Z归纳的”这个定义方案就变得有意义了。此外，已经证明了几个定理，它们似乎只是在z的实例中有所不同。当我们考虑诸如z连续性的z完备性等概念时，也会出现类似的现象。这表明在所有这些不同的情况下我们讨论的是相同的Z。在本文中，我们通过抽象出Z的不同实例的基本共同性质并在由此产生的抽象框架内证明共同定理来证明这确实是这种情况。
The definition scheme,“A poset P is Z-inductive if it has a subposet B of Z-compact lements such that for every element of p of P there is a Z-set S in B such that p=⨆ S, becomes meaningful when we replace the symbol of Z by such adjectives as “sirected”,“chain”,“pairwise compatible”,“singleton”, etc. Furthermore, several theorems have been proved that seem to differ only in their instantiations of Z. A simialr phenomena occurs when we comsider concepts such as Z-completeness of Z-comtinuity. This suggests that in all these different cases we are really talking about Z same thing. In this paper we show that this is indeed the case by abstracting out the essential common properties of the different instantiations of Z and proving common theorems within the resulting abstract framework.