A generalized Cantor theorem in ZF

TL;DR

This paper proves in ZF set theory that for any infinite set, there are no surjections from the product of omega and that set onto its power set, extending Cantor's theorem without relying on the axiom of choice.

Contribution

It establishes a generalized form of Cantor's theorem within ZF, demonstrating the non-existence of certain surjections without the axiom of choice.

Findings

No surjection from ω×M onto P(M) for infinite M in ZF.

Extends Cantor's theorem without the axiom of choice.

Clarifies limitations of set mappings in ZF.

Abstract

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