论逻辑与集合论的融合
On the Syntax of Logic and Set Theory
摘要：
我们介绍了一个扩展的命题演算，包括抽象的谓词和量词，采用一个单一的规则，以及一个新的理解模式和原则的外延性，这是取代伯奈斯假设的量词和理解模式的ZF和其他集合论。我们证明了它在任何有限布尔子集格中是相容的。我们调查的二律背反罗素，康托，Burali-Forti，和其他人，并讨论了系统的关系，其他集理论系统ZF，NBG和NF。我们讨论了公理化高阶量化和抽象的两种方法，然后非常简要地讨论了其中一种方法在逻辑之外的数学领域的应用。
英文摘要：
We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the Bernays postulates for quantifiers and the comprehension schemata of ZF and other set theories. We prove that it is consistent in any finite Boolean subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti, and others, and discuss the relationship of the system to other set theoretic systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order quantification and abstraction, and then very briefly discuss the application of one of these methods to areas of mathematics outside of logic.
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