### Examples for Souslin Forcing

by Judah and Roslanowski and Shelah. [JRSh:373]

Fundamenta Math, 1994

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.

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