Algebraic Properties of Generalized Multisets

A. Alexandru, Gabriel Ciobanu
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引用次数: 8

Abstract

We present generalized multisets in the Zermelo-Fraenkel framework, in Reverse Mathematics, and in the Fraenkel-Mostowski framework. In the Zermelo-Fraenkel framework, we prove that the set of all generalized multisets over a certain finite set is a finitely-generated, lattice-ordered, free abelian group. Similar properties are then discussed in Reverse Mathematics. Finally, we study the generalized multisets in the Fraenkel-Mostowski framework, and present their nominal properties. Several Zermelo-Fraenkel algebraic properties of generalized multisets are translated into the Fraenkel-Mostowski framework by using the finite support axiom of the Fraenkel-Mostowski set theory.
广义多集的代数性质
我们在Zermelo-Fraenkel框架、逆向数学和Fraenkel-Mostowski框架中提出了广义多集。在Zermelo-Fraenkel框架下,证明了某有限集合上所有广义多集的集合是一个有限生成的格序自由阿贝尔群。然后在逆向数学中讨论类似的性质。最后,我们研究了Fraenkel-Mostowski框架下的广义多集,并给出了它们的名义性质。利用Fraenkel-Mostowski集合论的有限支持公理,将广义多集的几个Zermelo-Fraenkel代数性质转化为Fraenkel-Mostowski框架。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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