On a cardinal inequality in ZF $\mathsf {ZF}$

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2023-08-04 DOI:10.1002/malq.202300014

Guozhen Shen

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引用次数: 1

Abstract

It is proved in $ZF$ (without the axiom of choice) that $a^{n} ⩽ S_{n + 1} (a)$ for all infinite cardinals $a$ and all natural numbers $n \neq 0$ , where $S_{n + 1} (a)$ is the cardinality of the set of permutations with exactly $n + 1$ non-fixed points of a set which is of cardinality $a$ .

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关于ZF $\mathsf {ZF}$中的基数不等式

这是proved in 安迪是 $\ mathsf{安迪是 }$ ( 那没有选择公理》) a n ⩽ S n + 1 ( a) $\ mathfrak {a} ^ n的leqslant \ mathcal {S} {n + 1} (\ mathfrak {a })$ 为所有无限红雀队 a $\ mathfrak {a }$ 和所有自然的数字 n ≠ 0 $ n \ ne 0 $ ,哪里是n+1 (a1美元n+1美元非固定点a $ mathfrak

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.