论布尔代数的公理系统与公理的独立性

On the Axiom Systems and the Independence of Axioms for Boolean Algebras

朱秉涛在文“关于布尔代数公理的独立性问题”中认为由Hunttngton E. V.提出的关于布尔代数的八条公理是相互独立的这一结论是错误的。本文将论证朱的这一结论是错误的,也即Huntington的关于布尔代数的八条公理的确是相互独立的。另外本文还提供关于布尔代数的其它两个公理系统,它们的各公理不但仍是相互独立的,且从某种意义上讲,它们比Huntington的优越。

In the reference [1] the author concludes that the conclusion in the references [2, 3], i. e. eight axioms for Boolean algebras due to E. V. Huntington are each other independent, is wrong. We take it that Huntington's eight axioms for Boolean algebra are dependent. Indeed, the conclusion of the reference[1]is mistaken, and the conclusion in the reference [2, 3]is correct. We propose also other two axiom systems for Boolean algebra which are also independent.