Hi Richard, have you looked at Laver's work on elementary embeddings of ranks and left distributive operations? (Bourbaki swerve: Large cardinals ahead.) It is from the early 90's. I think that the main paper was published in the Advances, or the Annals. Patrick Dehornoy (a name you might know from Funk's 2001 paper in TAC, on the Hurwitz action and braid group orderings) has written some expository material around this stuff, most if not all of which is available on his web page.
