CANTOR SETS AND FIELDS OF REALS

被引：0
|
作者：
Kuba, Gerald [1 ]
机构：
[1] Univ Nat Resources & Life Sci, Inst Math, Vienna, Austria
来源：
MATEMATICKI VESNIK | 2022年 / 74卷 / 04期
关键词：
Transcendental extensions; descriptive set theory;
D O I：
10.57016/MV-ywug8949
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Our main result is a construction of four families C1, C2, B1, B2 which are equipollent with the power set of R and satisfy the following properties. (i) The members of the families are proper subfields K of R where R is algebraic over K. (ii) Each field in C-1 boolean OR C-2 contains a Cantor set. (iii) Each field in B-1 boolean OR B-2 is a Bernstein set. (iv) All fields in C-1 boolean OR B-1 are isomorphic. (v) If K, L are fields in C2. B2 then K is isomorphic to some subfield of L only in the trivial case K = L.
引用
收藏
页码：249 / 259
页数：11
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