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.
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Laguzzi, G. Some considerations on amoeba forcing notions. Arch. Math. Logic 53, 487–502 (2014). https://doi.org/10.1007/s00153-014-0375-x
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DOI: https://doi.org/10.1007/s00153-014-0375-x