# Sh:373

- Judah, H. I., Rosłanowski, A., & Shelah, S. (1994).
*Examples for Souslin forcing*. Fund. Math.,**144**(1), 23–42. arXiv: math/9310224 DOI: 10.4064/fm-144-1-23-42 MR: 1271476 -
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. - Version 1996-03-17_10 (26p) published version (20p)

Bib entry

@article{Sh:373, author = {Judah, Haim I. and Ros{\l}anowski, Andrzej and Shelah, Saharon}, title = {{Examples for Souslin forcing}}, journal = {Fund. Math.}, fjournal = {Fundamenta Mathematicae}, volume = {144}, number = {1}, year = {1994}, pages = {23--42}, issn = {0016-2736}, mrnumber = {1271476}, mrclass = {03E40 (03E15 03E35 04A15)}, doi = {10.4064/fm-144-1-23-42}, note = {\href{https://arxiv.org/abs/math/9310224}{arXiv: math/9310224}}, arxiv_number = {math/9310224} }