I have read the Wikipedia article on the Lévy hierarchy. It mentions a few large cardinal axioms, but it does not mention any of the rank-into-rank axioms. So I have the following questions:
- what is the complexity (in the Lévy hierarchy) of the axiom $\text{I0}$?
- Is there any source (a book/paper) that provides the axiom $\text{I0}$ written in some formal language (similar to how this article on Wikipedia provides the descriptions of the axioms of ZF)?
- What can be an example of a formal language that allows to formulate the axiom $\text{I0}$?