On uncountable strongly concentrated sets of reals

TL;DR

This paper constructs new models of ZF set theory featuring an uncountable set of reals with a single condensation point, addressing a question posed by Sierpiński in 1918.

Contribution

It introduces novel models of ZF with uncountable sets of reals having a unique condensation point, solving a long-standing open problem.

Findings

Existence of uncountable sets of reals with a unique condensation point in ZF models

Addresses Sierpiński's 1918 question about condensation points

Provides new insights into the structure of uncountable sets of reals

Abstract

We construct new models of $ZF$ with an uncountable set of reals that has a unique condensation point. This addresses a question by Sierpi\'{n}ski from 1918.