Another proof of a result of Jech and Shelah

Shelah’s pcf theory describes a certain structure which must exist if is strong limit and holds. Jech and Shelah proved the surprising result that this structure exists in ZFC. They first give a forcing extension in which the structure exists then argue that by some absoluteness results it must exist anyway. We reformulate the statement to the existence of a certain partially ordered set, and then we show by a straightforward, elementary (i.e., non-metamathematical) argument that such partially ordered sets exist.