I would like to ask what the specific novel modeltheoretic (or settheoretic) techniques, if any, are that Mochizuki uses in his recent series of four papers. Section 3 of Interuniversal Teichmüller Theory IV, as well as the comments on page 21 of paper I, seem to suggest that there are modeltheoretic techniques in play; I don't, unfortunately, have the background in algebraic geometry to understand the presentation.
