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  1. Piece selection and cardinal arithmetic.Pierre Matet - 2022 - Mathematical Logic Quarterly 68 (4):416-446.
    We study the effects of piece selection principles on cardinal arithmetic (Shelah style). As an application, we discuss questions of Abe and Usuba. In particular, we show that if λ ≥ 2 κ $\lambda \ge 2^\kappa$, then (a) I κ, λ $I_{\kappa, \lambda }$ is not (λ, 2)-distributive, and (b) I κ, λ + → ( I κ, λ + ) ω 2 $I_{\kappa, \lambda }^+ \rightarrow (I_{\kappa, \lambda }^+)^2_\omega$ does not hold.
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