Piece selection and cardinal arithmetic

IF 0.4 4区数学 Q4 LOGIC

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

Pierre Matet

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引用次数: 0

Abstract

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.

查看原文本刊更多论文

棋子选择和基数算术

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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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.