Adding a club with finite conditions, Part II

Abstract

We define a forcing poset which adds a club subset of a given fat stationary set \({S \subseteq \omega_2}\) with finite conditions, using S-adequate sets of models as side conditions. This construction, together with the general amalgamation results concerning S-adequate sets on which it is based, is substantially shorter and simpler than our original version in Krueger (Arch Math Logic 53(1–2):119–136, 2014).