We will present an argument for reflecting the large cardinal axiom I_0 from marginally stronger large cardinals. This will involve presenting some of the theory of inverse limits, which R. Laver first studied in the context of reflecting large cardinals at this level. Along the way we will see many local reflection results below I_0 and state a strong form of reflection which is useful in other contexts.
Scott Cramer received his Ph.D. from the University of California-Berkeley in 2012, with a thesis on reflection of large cardinals, written under the supervision of Hugh Woodin. He is presently a Triennial Assistant Professor at Rutgers University, working in set theory, with specific interests in very large cardinals and determinacy axioms.