The Approachability Ideal Without a Maximal Set

John Krueger

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arXiv · 1607.04772

The Approachability Ideal Without a Maximal Set

John Krueger

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Abstract

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 $\omega_1$-approximation property. We apply these ideas to prove, assuming the consistency of a greatly Mahlo cardinal, that it is consistent that the approachability ideal $I[\omega_2]$ does not have a maximal set modulo clubs.

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BibTeX RIS

John Krueger. 2016-07-16. The Approachability Ideal Without a Maximal Set. https://arxiv.org/abs/1607.04772

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