Specializing Trees with Small Approximations I

Rahman Mohammadpour

Specializing Trees with Small Approximations I

Logic 2022-03-14 v2

Authors: Rahman Mohammadpour

Abstract

Assuming $\rm PFA$ , we shall use internally club $\omega_1$ -guessing models as side conditions to show that for every tree $T$ of height $\omega_2$ without cofinal branches, there is a proper and $\aleph_2$ -preserving forcing notion with finite conditions which specialises $T$ . Moreover, the forcing has the $\omega_1$ -approximation property.

Keywords

set theory forcing trees random trees

Cite

@article{arxiv.2101.01594,
  title  = {Specializing Trees with Small Approximations I},
  author = {Rahman Mohammadpour},
  journal= {arXiv preprint arXiv:2101.01594},
  year   = {2022}
}

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