Abstract-Definable closed unbounded sets, and specifically, ordinal definable ones, play a significant role in the study of canonical inner models of set theory and the class HOD of hereditarily ordinal definable sets. Fixing a certain notion of definability and an uncountable cardinal, one can consider the associated family of definable closed unbounded sets. We consider the extent to which such families can approximate the full closed unbounded filter, and their dependence on the defining complexity. This is a joint work with Philipp Lucke.