拟投射关系代数与有向柱形代数范畴等价
Quasi-projective relation algebras and directed cylindric algebras are categorially equivalent
摘要：
证明了拟投射关系代数与有向柱形代数范畴等价。本文给出了一阶逻辑有限变量片段的哥德尔第二不完全性定理。我们表明，不同的集合论（如CH，和另一个与它的否定）产生等式不同的简单定向柱形代数。这种对应关系是针对拟投射关系代数（具有一个对应于隶属关系的特殊元素）而得到的。证明的思想是：有向柱形代数的Sagi表示保持良基性。最后，利用函子保序的性质，证明了这类有向柱形代数具有超融合性质。
英文摘要：
We show that quasi-projective relation algebras and directed cylindric algebras are equivalent categorialy. We work out a Godels second incompleteness theorem for finite varibale fragments of first order logic. We show that distinct set theories (like one with CH, and another with its negation) give rise to equationally distinct simple directed cylindric algebras. This correspondance was worked out for quasi projective relation algebras (with a distinguished element corresponding to membership relation). The idea of the proof is that the Sagi representation of directed cylindric algebras preserve well-foundnes. Finally, using that the functor defined preserves order, we show that the class of directed cylindric algebras have the superamalgmation property.
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