A surjection from square onto power

TL;DR

This paper demonstrates that within ZF set theory, it is consistent for an infinite set to have its square map onto its power set, revealing interesting properties of infinite sets and their mappings.

Contribution

It establishes the consistency of a surjection from the square of an infinite set onto its power set within ZF, a novel result in set theory.

Findings

Existence of such a surjection is consistent with ZF.

Provides new insights into mappings between infinite sets and their power sets.

Challenges assumptions about the structure of infinite sets.

Abstract

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