Scott图模型和Kleene第二代数的推广
Extensions of Scott's Graph Model and Kleene's Second Algebra
摘要：
我们用一种方法来扩充部分组合代数，强迫它们表示某些函数。在Scott的Graph模型中，等式相对于补函数是可计算的。然而，反过来就不对了。这创建了一个pca的层次结构，它与其他pca上的扩展的类似结构相关。我们研究了一个这样的结构Kleene的第二个模型和一个PCA等价，但不同构于它。对于递归可重复的子PCA的图形模型，结果不同，因为我们可以计算（部分）补充功能使用的平等。
英文摘要：
We use a way to extend partial combinatory algebras (pcas) by forcing them to represent certain functions. In the case of Scott's Graph model, equality is computable relative to the complement function. However, the converse is not true. This creates a hierarchy of pcas which relates to similar structures of extensions on other pcas. We study one such structure on Kleene's second model and one on a pca equivalent but not isomorphic to it. For the recursively enumerable sub pca of the Graph model, results differ as we can compute the (partial) complement function using the equality.
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