On $ω_3$-chains in P($ω_1$) mod finite

Details On $ω_3$-chains in P($ω_1$) mod finite On $ω_3$-chains in P($ω_1$) mod finite

2008-11-04

arxiv.org/abs/0811.0548v2

Mathematics

Logic

There are some gaps in the proof which I am unable to fix

Scientific paper

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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