Banach's theorem in higher-order reverse mathematics

被引：0
|
作者：
Hirst, Jeffry L. [1 ]
Mummert, Carl [2 ]
机构：
[1] Appalachian State Univ, Dept Math Sci, Boone, NC 28608 USA
[2] Marshall Univ, Dept Comp & Informat Technol, Huntington, WV USA
来源：
COMPUTABILITY-THE JOURNAL OF THE ASSOCIATION CIE | 2023年 / 12卷 / 03期
关键词：
Reverse mathematics; Weihrauch reducibility; bijection; metric spaces;
D O I：
10.3233/COM-230453
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, methods of second-order and higher-order reverse mathematics are applied to versions of a theorem of Banach that extends the Schroder-Bernstein theorem. Some additional results address statements in higher-order arithmetic formalizing the uncountability of the power set of the natural numbers. In general, the formalizations of higher-order principles here have a Skolemized form asserting the existence of functionals that solve problems uniformly. This facilitates proofs of reversals in axiom systems with restricted choice.
引用
收藏
页码：203 / 225
页数：23
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