Archive for Mathematical Logic 53 (5-6):487-502 (2014)

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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DOI 10.1007/s00153-014-0375-x
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References found in this work BETA

Δ12-Sets of Reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
Solovay-Type Characterizations for Forcing-Algebras.Jörg Brendle & Benedikt Löwe - 1999 - Journal of Symbolic Logic 64 (3):1307-1323.
Generic Trees.Otmar Spinas - 1995 - Journal of Symbolic Logic 60 (3):705-726.
Borel Partitions of Infinite Subtrees of a Perfect Tree.A. Louveau, S. Shelah & B. Veličković - 1993 - Annals of Pure and Applied Logic 63 (3):271-281.

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Citations of this work BETA

Generalized Silver and Miller Measurability.Giorgio Laguzzi - 2015 - Mathematical Logic Quarterly 61 (1-2):91-102.
Full-Splitting Miller Trees and Infinitely Often Equal Reals.Yurii Khomskii & Giorgio Laguzzi - 2017 - Annals of Pure and Applied Logic 168 (8):1491-1506.
More on Trees and Cohen Reals.Giorgio Laguzzi & Brendan Stuber‐Rousselle - 2020 - Mathematical Logic Quarterly 66 (2):173-181.

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