On iterated forcing at successors of regular cardinals

Todd Eisworth

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On iterated forcing at successors of regular cardinals

Todd Eisworth

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Abstract

We investigate the problem of when $\leqλ$--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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BibTeX RIS

Todd Eisworth. 2002-10-10. On iterated forcing at successors of regular cardinals. https://arxiv.org/abs/math/0210162

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