ELA, Volume 7, pp. 41-52, May 2000, abstract.

Almost Disjoint Families: An Application to Linear Algebra

Oren Kolman

Suppose that k is an infinite cardinal, V is a k-dimensional vector space
over a field F, and A is a family of subspaces of V which is maximal with
respect to the property: whenever U and W are distinct members of A, then
U intersection W has dimension less than k. What is the cardinality of A?
This expository paper explains how questions about the possible cardinality
of A for vector spaces of infinite dimension over countable fields are
independent of the axioms of ordinary set theory (ZFC).