2016/07/16 by Krueger, John · 1 citation
#03E40 #FOS: Mathematics #Logic (math.LO) #Primary 03E35 #Secondary 03E05
paper · doi:10.48550/arxiv.1607.04772
We develop a forcing poset with finite conditions which adds a partial square sequence on a given stationary set, with adequate sets of models as side conditions. We then develop a kind of side condition product forcing for simultaneously adding partial square sequences on multiple stationary sets. We show that certain quotients of such forcings have the ω1-approximation property. We apply these ideas to prove, assuming the consistency of a greatly Mahlo cardinal, that it is consistent that the approachability ideal I[ω2] does not have a maximal set modulo clubs.