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arXiv · 0811.0548

On $\omega_3$-chains in P($\omega_1$) mod finite

Bernhard Irrgang
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Abstract

We prove that if there exists a simplified $(\omega_1,2)$-morass, then there is a ccc forcing which adds an $\omega_3$-chain in P($\omega_1$) mod finite and a ccc forcing which adds a family of $\omega_3$-many strongly almost disjoint functions from $\omega_1$ to $\omega$. The idea is to use a finite support iteration of countable forcings which is not linear but three-dimensional.

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Bernhard Irrgang. 2008-11-04. On $\omega_3$-chains in P($\omega_1$) mod finite. https://arxiv.org/abs/0811.0548

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