Autoepistemic (AE) logic is a formal system characterizing agents that have complete introspective access to their own beliefs. AE logic relies on a fixed point definition that has two significant parts. The first part is a set of assumptions or hypotheses about the contents of the fixed point. The second part is a set of reflection principles that link sentences with statements about their provability. We characterize a family of ideal AE reasoners in terms of the minimal hypotheses that they can make, and the weakest and strongest reflection principles that they can have, while still maintaining the interpretation of AE logic as self-belief. These results can help in analyzing metatheoretic systems in logic programming.