we study the complexity of the classification problem for cartan subalgebras in von neumann algebras. we will discuss a construction that leads to a family of ii$_1$ factors whose cartan subalgebras, up to unitary conjugacy, are not classifiable by countable structures. we do this via establishing a strong dichotomy, depending if the action is strongly ergodic or not, on the complexity of the space of homomorphisms from a given equivalence relation to $e_0$. we will start with some of the necessary preliminaries, and then outline the proofs of the aforementioned results.