Definable MAD families and forcing axioms
Vera Fischer, David Schrittesser, Thilo Weinert
TL;DR
This paper demonstrates the existence of a definable maximal almost disjoint family under certain forcing axioms and anti-large cardinal assumptions, contributing to the understanding of definability in set theory.
Contribution
It establishes the existence of a $oldsymbol{ ext{Pi}}^1_2$ MAD family assuming Bounded Proper Forcing Axiom and anti-large cardinal hypotheses, linking forcing axioms with definability.
Findings
Existence of a $oldsymbol{ ext{Pi}}^1_2$ MAD family under specified axioms
Connection between forcing axioms and definability of MAD families
Use of anti-large cardinal assumptions in the construction
Abstract
We show that under the Bounded Proper Forcing Axiom and an anti-large cardinal assumption, there is a MAD family.
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