A general tool for consistency results related to I1

preprint2015arXivOpen access

Abstract

In this paper we provide a general tool to prove the consistency of I1(λ)I1(λ) with various combinatorial properties at λλ typical at settings with 2λ>λ+2^λ>λ^+, that does not need a profound knowledge of the forcing notions involved. Examples of such properties are the first failure of GCH, a very good scale and the negation of the approachability property, or the tree property at λ+λ^+ and λ++λ^{++}.

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