Some structural similarities between uncountable sets, powersets and the universe

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2022-03-06 DOI:10.1002/malq.202100010

Athanassios Tzouvaras

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引用次数: 0

Abstract

We establish some similarities/analogies between uncountable cardinals or powersets and the class V of all sets. They concern mainly the Boolean algebras $P (κ)$ , for a regular cardinal κ, and $C (V)$ (the class of subclasses of the universe V), endowed with some ideals, especially the ideal ${[κ]}^{< κ}$ for $P (κ)$ , and the ideal of sets V for $C (V)$ .

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不可数集、幂集和全域之间的结构相似性

我们在不可数基数或幂集与所有集合的类V之间建立了一些相似/类比。它们主要涉及布尔代数P (κ)$ \mathcal {P}(\kappa)$，对于正则基数κ和C (V)$ \mathcal {C}(V)$(宇宙V的子类的类)，它们被赋予了一些理想。尤其是理想的[κ] <κ $[\kappa]^{<\kappa}$对于P (κ)$ \mathcal {P}(\kappa)$，以及集合V对于C (V)$ \mathcal {C}(V)$的理想。

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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.