棋子选择和基数算术

Pub Date : 2022-09-07 DOI:10.1002/malq.202100033

Pierre Matet

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引用次数: 0

摘要

我们研究了选片原则对基数算术(Shelah风格)的影响。作为一种应用，我们讨论了安倍和乌苏巴的问题。特别地，我们证明了如果λ≥2 κ $\lambda \ge 2^\kappa$，则(a) I κ， λ $I_{\kappa , \lambda }$不是(λ， 2)-分布的，(b) I κ， λ +→(I κ，λ +) ω 2 $I_{\kappa , \lambda }^+ \rightarrow (I_{\kappa , \lambda }^+)^2_\omega$不成立。

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Piece selection and cardinal arithmetic

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 $λ \geq 2^{κ}$ , then (a) $I_{κ, λ}$ is not (λ, 2)-distributive, and (b) $I_{κ, λ}^{+} \to {(I_{κ, λ}^{+})}_{ω}^{2}$ does not hold.

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