# Stranger Things about Forcing without AC

## TL;DR

This paper explores how certain properties of forcing posets fail in ZF set theory without the Axiom of Choice, providing insights into the limitations of forcing in the absence of AC.

## Contribution

It demonstrates that key properties of forcing posets do not hold without the Axiom of Choice, answering a question posed by Miller.

## Key findings

- Several properties of forcing posets fail without AC
- Answers Miller's question from arXiv:0704.3998
- Highlights limitations of forcing in ZF set theory

## Abstract

Typically, set theorists reason about forcing constructions in the context of ZFC. We show that without AC, several simple properties of forcing posets fail to hold, one of which answers Miller's question from arXiv:0704.3998.

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Source: https://tomesphere.com/paper/1706.01708