康托集与实数域
Cantor sets and fields of reals
摘要：
我们的主要结果是构造了四个族C_1，C_2，B_1，B_2，它们等价于实直线R的幂集并满足下列性质。(i)族的成员是R的真子域，其代数闭包等于域C。(ii)C_1 vC_2中的每个字段包含一个康托尔集。(iii)B_1vB_2中的每个字段都是伯恩斯坦集。(iv)C_1vB_1中的所有域都是同构的。(v)若K，L是C_2vB_2中的域，则K仅在平凡情形K=L时同构于L的子域.
英文摘要：
Our main result is a construction of four families C_1,C_2,B_1,B_2 which are equipollent with the power set of the real line R and satisfy the following properties. (i) The members of the families are proper subfields of R whose algebraic closures equal the field C. (ii) Each field in C_1vC_2 contains a Cantor set. (iii) Each field in B_1vB_2 is a Bernstein set. (iv) All fields in C_1vB_1 are isomorphic. (v) If K,L are fields in C_2vB_2 then K is isomorphic to a subfield of L only in the trivial case K=L.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
