Adding Club Subsets of Ω 2 Using Conditions with Finite Working Parts

After a couple of weeks I eventually got around to reading the preprint and started wondering about recasting the argument in my preferred formalism. I arrogantly assumed that this would allow one to smooth out parts of the proof and simplify the details of the definition of the forcing conditions (at the cost of taking the framework set out in §§1,2 below as given). However when I tried to write things down I found myself, to my chagrin, more or less cornered in making my definitions into most of the intricacies that Friedman had been. I suppose that this shows that the original proof is in some sense the natural one (or one of a family of ‘natural’ ones). Nevertheless I obstinately persisted and this note is the result.