Examples for Souslin forcing

Examples for Souslin Forcing

Forcing with a Coherent Souslin Tree

We investigate the effect of forcing with a coherent Souslin trees on two standard set-theoretic dichotomies and several topological chain conditions.

Ideals Determined by Some Souslin Forcing Notions

We describe a method of building “nice” σ–ideals from Souslin ccc forcing notions.

Changing the heights of automorphism towers by forcing with Souslin trees over L

We prove that there are groups in the constructible universe whose automorphism towers are highly malleable by forcing. This is a consequence of the fact that, under a suitable diamond hypothesis, there are sufficiently many highly rigid non-isomorphic Souslin trees whose isomorphism relation can be precisely controlled by forcing.

On full Souslin trees

In the present note we answer a question of Kunen (15.13 in [Mi91]) showing (in 1.7) that it is consistent that there are full Souslin trees. ∗ We thank the NSF for partially supporting this research under grant #144-EF67. Publication No 624.