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 interesting associated questions. Acknowledgement For the first part of the present paper, the author wishes to thank Sy Friedman and the FWF for the indispensable support through the research project #P22430-N13.