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

Bernhard Irrgang

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

Logic 2011-10-18 v2

Authors: Bernhard Irrgang

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.

Keywords

set theory forcing set theory

Cite

@article{arxiv.0811.0548,
  title  = {On $\omega_3$-chains in P($\omega_1$) mod finite},
  author = {Bernhard Irrgang},
  journal= {arXiv preprint arXiv:0811.0548},
  year   = {2011}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

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