Are a and d your cup of tea?

TL;DR

This paper proves that every MAD family has a size larger than the dominating number, resolving a longstanding open problem in cardinal invariants of the continuum using iterated forcing techniques.

Contribution

It establishes that all MAD families have cardinality greater than the dominating number, advancing the understanding of the structure of the continuum.

Findings

MAD families have cardinality strictly greater than the dominating number

Introduces a method using iterated forcing to analyze continuum cardinalities

Solves a longstanding open problem in set theory

Abstract

We show that, consistently, every MAD family has cardinality strictly bigger than the dominating number, that is a > d, thus solving one of the oldest problems on cardinal invariants of the continuum. The method is a contribution to the theory of iterated forcing for making the continuum large.