CONSTRUCTING MAXIMAL COFINITARY GROUPS

被引：1
|
作者：
Schrittesser, David [1 ,2 ]
机构：
[1] Univ Toronto, Dept Math, 40 St George St, Toronto, ON M5S 2E4, Canada
[2] Harbin Inst Technol, Inst Adv Study Math, 92 West Da Zhi St, Harbin 150001, Heilongjiang, Peoples R China
来源：
NAGOYA MATHEMATICAL JOURNAL | 2023年
基金：
奥地利科学基金会;
关键词：
maximal cofinitary groups; definability; arithmetic; Borel; Axiom of Choice; PERMUTATION-GROUPS;
D O I：
10.1017/nmj.2022.46
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Improving and clarifying a construction of Horowitz and Shelah, we show how to construct (in ZF , i.e., without using the Axiom of Choice) maximal cofinitary groups. Among the groups we construct, one is definable by a formula in second-order arithmetic with only a few natural number quantifiers.
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页码：622 / 651
页数：30
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