Examples for Souslin forcing
Logic
2016-09-06 v1
Abstract
We give a model where there is a ccc Souslin forcing which does not satisfy the Knaster condition. Next, we present a model where there is a sigma-linked not sigma-centered Souslin forcing such that all its small subsets are sigma-centered but Martin Axiom fails for this order. Furthermore, we construct a totally nonhomogeneous Souslin forcing and we build a Souslin forcing which is proper but not ccc that does not contain a perfect set of mutually incompatible conditions. Finally we show that ccc Sigma^1_2-notions of forcing may not be indestructible ccc.
Keywords
Cite
@article{arxiv.math/9310224,
title = {Examples for Souslin forcing},
author = {Haim Judah and Andrzej Rosłanowski and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9310224},
year = {2016}
}