The question is exactly that of the title: what are Moschovakis cardinals?

**Background**. In a recent answer to the question, "Are there examples of statements that have been proven whose consistency proofs came before their proofs?," user14111 posted (https://mathoverflow.net/questions/71201/are-there-examples-of-statements-that-have-been-proven-whose-consistency-proofs/137218#137218) an answer involving "Moschovakis cardinals," a large cardinal notion which was shown to be inconsistent at some point in time. Now, googling for Moschovakis cardinals reveals nothing besides that answer and this (http://mathforum.org/kb/thread.jspa?forumID=13&threadID=22263&messageID=59655#59655) Math Forum Discussion post, which seems(?) to be responding to a post which was then deleted.

According to user14111, the notion of a Moschovakis cardinal arose in an unpublished manuscript circulated around the late 60s; given the timing, my current guess is that "Moschovakis cardinal" is just a synonym for "Reinhardt cardinal," but I'll admit there is no real basis for my guess.

**Why I'm interested**. (Assuming these aren't just Reinhardts in disguise) I'm always interested in large cardinal axioms inconsistent with ZFC; in particular, can Moschovakis cardinals survive in ZF? Also, on a purely historical level, it would be interesting to know about.

Even if Moschovakis=Reinhardt, I'm still intrigued: why would that name be used? I've heard Reinhardt cardinals called Kunen cardinals before, since Kunen proved their inconsistency; but Moschovakis seems to have no relation to the subject that I'm aware of.