Examples for Souslin forcing

Details Examples for Souslin forcing Examples for Souslin forcing

1993-10-15

arxiv.org/abs/math/9310224v1

Fund. Math. 144 (1994), 23--42

Mathematics

Logic

Scientific paper

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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