Algebraic Properties of Generalized Multisets

Author

Alexandru, Andrei ; Ciobanu, Gabriel

Author_Institution

Inst. of Comput. Sci., Iasi, Romania

fYear

2013

fDate

23-26 Sept. 2013

Firstpage

367

Lastpage

374

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.

Keywords

group theory; Fraenkel-Mostowski framework; Fraenkel-Mostowski set theory; Zermelo-Fraenkel framework; algebraic properties; finite support axiom; finitely-generated group; free Abelian group; generalized multisets; lattice-ordered group; nominal properties; reverse mathematics; Computational modeling; Computer science; Lattices; Set theory; Standards; Vectors; Reverse Mathematics; finitely supported objects; generalized multisets; lattice-ordered groups; nominal sets;

fLanguage

English

Publisher

ieee

Conference_Titel

Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2013 15th International Symposium on

Conference_Location

Timisoara

Print_ISBN

978-1-4799-3035-7

Type

conf

DOI

10.1109/SYNASC.2013.55

Filename

6821172