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  1. Higher Miller forcing may collapse cardinals.Heike Mildenberger & Saharon Shelah - 2021 - Journal of Symbolic Logic 86 (4):1721-1744.
    We show that it is independent whether club $\kappa $ -Miller forcing preserves $\kappa ^{++}$. We show that under $\kappa ^{ \kappa $, club $\kappa $ -Miller forcing collapses $\kappa ^{<\kappa }$ to $\kappa $. Answering a question by Brendle, Brooke-Taylor, Friedman and Montoya, we show that the iteration of ultrafilter $\kappa $ -Miller forcing does not have the Laver property.
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  • More on trees and Cohen reals.Giorgio Laguzzi & Brendan Stuber-Rousselle - 2020 - Mathematical Logic Quarterly 66 (2):173-181.
    In this paper we analyse some questions concerning trees on κ, both for the countable and the uncountable case, and the connections with Cohen reals. In particular, we provide a proof for one of the implications left open in [6, Question 5.2] about the diagram for regularity properties.
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