Antichains of perfect and splitting trees

Archive for Mathematical Logic 59 (3-4):367-388 (2020)
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Abstract

We investigate uncountable maximal antichains of perfect trees and of splitting trees. We show that in the case of perfect trees they must have size of at least the dominating number, whereas for splitting trees they are of size at least \\), i.e. the covering coefficient of the meager ideal. Finally, we show that uncountable maximal antichains of superperfect trees are at least of size the bounding number; moreover we show that this is best possible.

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Citations of this work

On splitting trees.Giorgio Laguzzi, Heike Mildenberger & Brendan Stuber-Rousselle - 2023 - Mathematical Logic Quarterly 69 (1):15-30.
Different cofinalities of tree ideals.Saharon Shelah & Otmar Spinas - 2023 - Annals of Pure and Applied Logic 174 (8):103290.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Sacks forcing, Laver forcing, and Martin's axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.
Generic trees.Otmar Spinas - 1995 - Journal of Symbolic Logic 60 (3):705-726.

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