Lusin set
= Lusin set
{c}
{title2=$|A\cap M|\leq\aleph_0\text{ for every meagre }M$}
A Lusin set is an uncountable <subset> $A$ of the <real numbers> such that $A\cap M$ is countable for every <meagre set> $M$. Every meagre subset has a meagre $F_\sigma$ cover, so testing those covers suffices. The <Lusin set construction under CH> gives an example. A Lusin set has no uncountable meagre subset of itself.