Silver Antichains

Journal of Symbolic Logic 80 (2):503-519 (2015)
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Abstract

In this paper we investigate the structure of uncountable maximal antichains of Silver forcing and show that they have to be at least of size d, where d is the dominating number. Part of this work can be used to show that the additivity of the Silver forcing ideal has size at least the unbounding number b. It follows that every reasonable amoeba Silver forcing adds a dominating real.

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Citations of this work

Different cofinalities of tree ideals.Saharon Shelah & Otmar Spinas - 2023 - Annals of Pure and Applied Logic 174 (8):103290.
Full-splitting Miller trees and infinitely often equal reals.Yurii Khomskii & Giorgio Laguzzi - 2017 - Annals of Pure and Applied Logic 168 (8):1491-1506.
Antichains of perfect and splitting trees.Paul Hein & Otmar Spinas - 2020 - Archive for Mathematical Logic 59 (3-4):367-388.
No Tukey reduction of Lebesgue null to Silver null sets.Otmar Spinas - 2018 - Journal of Mathematical Logic 18 (2):1850011.

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References found in this work

Sacks forcing, Laver forcing, and Martin's axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.
Some considerations on amoeba forcing notions.Giorgio Laguzzi - 2014 - Archive for Mathematical Logic 53 (5-6):487-502.
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.
More forcing notions imply diamond.Andrzej Rosłanowski & Saharon Shelah - 1996 - Archive for Mathematical Logic 35 (5-6):299-313.

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