模糊范畴fuz中的选择公理  

The Axioms of Choice in Fuzzy Category fuz

作　　者：王潇扬 王宝山[1] 王拥军[1] 周恒 WANG Xiao-yang;WANG Bao-shan;WANG Yong-jun;ZHOU Heng(Beihang University,Beijing 100191,China)

机构地区：[1]北京航空航天大学数学与系统科学学院

出　　处：《模糊系统与数学》2019年第4期21-27,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(11371044)

摘　　要：Topos结构是范畴论中刻画集合论的强有力工具,AC1和AC2是topos中选择公理的两种表达形式.模糊范畴fuz不是topos,仅有一个弱topos的结构,在fuz中有两个相对应的等价的选择公理WAC1和WAC2.在此基础上,本文给出两个加强的选择公理WAC1′和WAC2′,并证明其等价性,最后给出了弱topos中的广义选择公理GWAC1′和GWAC2′的表达形式.Topos structure is a fundamental tool to describe set theory in category theory. There are two forms of axioms, AC1 and AC2, to express as the choice axioms in topos. The category fuz does not form a topos, it belongs to a structure called weak topos. Two axioms of choice WAC1 and WAC2 are equivalent in fuz, we strengthen these axioms as WAC1′ and WAC2′, then give the equivalence of such axioms. Finally, we put forward GWAC1′ and GWAC2′ as two forms of axioms of choice in weak topos.

关 键 词：范畴论 TOPOS 模糊集 选择公理 

分 类 号：O154[理学—数学]