# On the non-existence of $\kappa$-mad families

## TL;DR

This paper demonstrates the non-existence of -mad families in a specific set-theoretic model constructed from a supercompact cardinal, advancing understanding of combinatorial set theory under weaker axioms.

## Contribution

It constructs a model of ZF+DC_{} where -mad families do not exist, using large cardinal assumptions and forcing techniques.

## Key findings

- No -mad families in the constructed model
- Supports the consistency of non-existence of -mad families under ZF+DC_{}
- Extends set theory by linking large cardinals to combinatorial properties

## Abstract

Starting from a model with a Laver-indestructible supercompact cardinal $\kappa$, we construct a model of $ZF+DC_{\kappa}$ where there are no $\kappa$-mad families.