There is a $+$-Ramsey \textsf{MAD} family

TL;DR

This paper constructs a $+$-Ramsey MAD family within ZFC and shows that Miller-indestructible MAD families are also $+$-Ramsey, advancing understanding of their properties.

Contribution

It provides a ZFC construction of a $+$-Ramsey MAD family and proves that Miller-indestructibility implies $+$-Ramseyness, improving previous results.

Findings

Constructed a $+$-Ramsey MAD family in ZFC.

Proved Miller-indestructible MAD families are $+$-Ramsey.

Answered an open question of Michael Hrušák.

Abstract

We answer an old question of Michael Hru\v{s}\'{a}k by constructing a $+$-Ramsey \textsf{MAD} family without the need of any additional axioms beyond $\mathsf{ZFC.}$ We also prove that every Miller-indestructible \textsf{MAD }family is $+$-Ramsey, this improves a result of Michael Hru\v{s}\'{a}k.