Some considerations on amoeba forcing notions

Some considerations on amoeba forcing notions

In this paper we analyse some notions of amoeba for tree forcings. In particular we introduce an amoeba-Silver and prove that it satisfies quasi pure decision but not pure decision. Further we define an amoeba-Sacks and prove that it satisfies the Laver property. We also show some application to regularity properties. We finally present a generalized version of amoeba and discuss some interesti...

Ideals Determined by Some Souslin Forcing Notions

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

On Nicely Definable Forcing Notions

We prove that if Q is a nw-nep forcing then it cannot add a dominating real. We also show that amoeba forcing cannot be P(X)/I if I is an א1-complete ideal. Furthermore, we generalize the results of [12].

Simple Forcing Notions and Forcing Axioms

On Nicely Definable Forcing Notions Sh711

We prove that if Q is a nw-nep forcing then it cannot add a dominating real. We also show that amoeba forcing cannot be P(X)/I if I is an א1-complete ideal. Furthermore, we generalize the results of [Sh 480]. I would like to thank Alice Leonhardt for the beautiful typing. This research was partially supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanit...