The complexity of non-stationary ideals

Abstract

We present an overview of results on the question of whether the non-stationary ideal of an uncountable regular cardinal $\hat{I}º$ can be defined by a ${\hat{I}}_1$-formula using parameters of hereditary cardinality at most $\hat{I}º$. These results show that this question is deeply connected to several central topics of current research in set theory.

Survey paper. Revised version. 26 pages