Some structural similarities between uncountable sets, powersets and the universe

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

Athanassios Tzouvaras

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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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