On iterated forcing at successors of regular cardinals

2002/10/10 by Todd Eisworth, Eisworth, Todd
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/0210162

arxiv created 2002/10/10 · arxiv updated 2009/11/30

Abstract

We investigate the problem of when ≤λ--support iterations of <λ--complete notions of forcing preserve λ⁺. We isolate a property -- \em properness over diamonds -- that implies λ⁺ is preserved and show that this property is preserved by λ--support iterations. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder systems on \δ<λ⁺:\cf(δ)=λ\ that complements a theorem of Shelah.

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