Boole代数的等价刻画.PDFVIP

( ) , 27 , 3 , 169- 172, 179 , 2007 9 Journal of Baoji University of Arts and S ien es ( Natural S ien e) , Vol. 27, No. 3, pp. 169- 172, 179, Sept. 2007 * Boole 1, 2 1 段景瑶 , 王国俊 ( 1. , 7 10062; 2. , 7210 13) : 给出Boole 代数的等价刻画, 揭示 Boole 代数和二值命题逻辑的另 一种内在联系, Boole 代数更便捷地和其他代数联系 从二值逻辑的公理集入手, 运用推理, 证明, 举例的方 法进行了讨论 得出了Boole 代数的等价刻画以及等价刻画中各条公理的独立性. 并且利用等 价刻画, 讨论了Boole 代数与其它代数的关系 Boole 代数新定义的引入为进 一步认识和研究 Boole 代数提供了新的途径 : Boole 代数; 公理集; 独立性 : O 141. 1 : A : 1007- 1261( 2007) 03-0169-04 Equivalent characterization of Boolean algebra 1, 2 1 DUAN Jing- yao , WANG Guo-jun ( 1. Coll. Math. Infm. S i. , Shaanx i Normal Univ . , Xian 7 10062, Shaanx i, China; 2. Dept. Math. , Baoji Univ. Arts S i. , Baoji 721013, Shaanx i, China) Abstract: Aim To dis uss equivalent hara terization of Boolean algebra and show the relation betw een Boolean algebra and logi system L and some other algebra system s. Methods Inferen e, proof, and examples are used to dis uss the pr oblem. Results Ax ioms of equivalent hara terization is simplest and w hi h is proved to be equivalent to the Boolean algebra. The relationships among Boole- an algebra and some other algebra systems ar e also dis ussed. Conclusion T his equivalent hara ter- ization offer s a new w ay for us to investigate Boolean algebra from a new angle. Key words:Boolean algebra; ax iom set; independen e MSC 000:03G08 , Boole L Boole, Lukasiewi eM V ( ? , y ) , L * R 0 1 L , Boole [ 2]