Abstract Corrected Iterations

2023/02/16 by Horowitz, Haim, Shelah, Saharon
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2302.08581

Abstract

We consider (<λ)-support iterations of a version of (<λ)-strategically complete λ⁺-c.c. definable forcing notions along partial orders. We show that such iterations can be corrected to yield an analog of a result by Judah and Shelah for finite support iterations of Suslin ccc forcing, namely that if (ℙ_α, \underset∼\mathbb Q_β : α≤ δ, β<δ) is a FS iteration of Suslin ccc forcing and U⊆ δ is sufficiently closed, then letting ℙ_U be the iteration along U, we have ℙ_U \lessdot ℙ_δ.

Related

• Corrected Iteration
• Modern Forcing Techniques related to Finite Support Iteration: Ultrapowers, templates, and submodels
• More on forcing iteration
• Not collapsing cardinals <= kappa in (< kappa) --support iterations
• Morasses and finite support iterations