关于k-Suslin树的自乘积树

ON THE PRODUCT OF k-SUSLIN TREES

在定义了一般树的乘积树以后，讨论了文献［１］中关于ｋ－Ｓｕｓｌｉｎ树的自乘积树的一个命题．证明了当ｋ为正则基数时，ｋ－Ｓｕｓｌｉｎ树的自乘积树不再是ｋ－Ｓｕｓｌｉｎ树，并构造了一个ω－Ｓｕｓｌｉｎ树，其自乘积树仍然是ω－Ｓｕｓｌｉｎ树．

in this paper,under the condition that the product of general trees had been defind,wediscussed a sentence about the product of k-Suslin trees in reference [1]. It was shown that if kis regular and T is a k-Suslin tree, then T T is not a k-Suslin tree, and an ω-Suslin 2tree wasgiven to show that if K is singular, then T T can be k-Suslin tree.