arXiv 1607.047722016-07math.LO

The Approachability Ideal Without a Maximal Set

John Krueger

英文摘要：

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 $ω_1$-approximation property. We apply these ideas to prove, assuming the consistency of a greatly Mahlo cardinal, that it is consistent that the approachability ideal $I[ω_2]$ does not have a maximal set modulo clubs.

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