Abstract

We extend the results of Laver on using inverse limits to reflect large cardinals of the form, there exists an elementary embedding Lα → Lα. Using these inverse limit reflection embeddings directly and by broadening the collection of U-representable sets, we prove structural results of L under the assumption that there exists an elementary embedding j : L → L. As a consequence we show the impossibility of a generalized inverse limit X-reflection result for X ⊆ Vλ+1, thus focusing the study of L generalizations on L.