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.
Some considerations on amoeba forcing notions
Laguzzi G.
2014-01-01
Abstract
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.File in questo prodotto:
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