An Iteration Theorem for $\omega_1$-preserving Forcings

Andreas Lietz

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arXiv · 2403.09018

An Iteration Theorem for $\omega_1$-preserving Forcings

Andreas Lietz

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Abstract

We prove an iteration theorem which guarantees for a wide class of nice iterations of $\omega_1$-preserving forcings that $\omega_1$ is not collapse, at the price of needing large cardinals to burn as fuel. More precisely, we show that a nice iteration of $\omega_1$-preserving forcings which force SRP at successor steps and preserves old stationary sets does not collapse $\omega_1$.

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Andreas Lietz. 2024-03-14. An Iteration Theorem for $\omega_1$-preserving Forcings. https://arxiv.org/abs/2403.09018

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