On the logarithmic probability that a random integral ideal is $mathscr A$-free

This extends a theorem of Davenport and Erdos on sequences of rational integers to sequences of integral ideals in arbitrary number fields $K$. More precisely, we introduce a logarithmic density for sets of integral ideals in $K$ and provide a formula for the logarithmic density of the set of so-called $mathscr A$-free ideals, i.e. integral ideals that are not multiples of any ideal from a fixed set $mathscr A$.