G. Shen

A function is boundedly finite-to-one if there is a natural number $k$ such that each point has at most $k$ inverse images. In this paper, we prove in $ZF$ (i.e., the Zerm…

math.LO2023

Cantor's theorem may fail for finitary partitions

Guozhen Shen

A partition is finitary if all its members are finite. For a set $A$ , $B (A)$ denotes the set of all finitary partitions of $A$ . It is shown consistent with $ZF$ …

math.LO2022

A surjection from square onto power

Yinhe Peng, Guozhen Shen, Liuzhen Wu

It is shown that the existence of an infinite set $A$ such that $A^{2}$ maps onto $2^{A}$ is consistent with $ZF$ .

math.LO2021★ 1 cited

A generalized Cantor theorem in ZF

Yinhe Peng, Guozhen Shen

It is proved in $ZF$ (without the axiom of choice) that, for all infinite sets $M$ , there are no surjections from $ω \times M$ onto $P (M)$ .

math.LO2019★ 2 cited

A choice-free cardinal equality

Guozhen Shen

For a cardinal $a$ , let $fin (a)$ be the cardinality of the set of all finite subsets of a set which is of cardinality $a$ . It is proved wi…

math.LO2018★ 9 cited

Factorials of infinite cardinals in ZF

Guozhen Shen, Jiachen Yuan

For a set $x$ , let $S (x)$ be the set of all permutations of $x$ . We study several aspects of this notion in $ZF$ . The main results are as follows: (1) $\mathsf{Z…

On ordering of surjective cardinals

The finitary partitions with n non-singleton blocks of a set

A note on surjective cardinals

Boundedly finite-to-one functions

Cantor's theorem may fail for finitary partitions

A surjection from square onto power

A generalized Cantor theorem in ZF

A choice-free cardinal equality

Factorials of infinite cardinals in ZF

The finitary partitions with $n$ non-singleton blocks of a set