Moti Gitik give a talk “On a certain PCF configuration” with a proof that (2) is

consistently false (from quite weak hypotheses, at the level of strong cardinals). I

saw him again in Bristol back in September and the proof was still standing. ]]>

I do. 🙂

]]> In fact the construction of the sets gives that each one is a cofinal subset of with order type , so that “the first five elements of ” already makes

perfect sense.