{"title":"Algebraic Properties of Generalized Multisets","authors":"A. Alexandru, Gabriel Ciobanu","doi":"10.1109/SYNASC.2013.55","DOIUrl":null,"url":null,"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.","PeriodicalId":293085,"journal":{"name":"2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","volume":"28 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2013 15th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SYNASC.2013.55","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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.
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