Abstract

We study generalized multisets (multisets that allow possible negative multiplicities) both in the Zermelo-Fraenkel framework and in the finitely supported mathematics. We extend the notion of generalized multiset over a finite alphabet, and we replace it by the notion of algebraically finitely supported generalized multiset over a possibly infinite alphabet. We analyze the correspondence between some properties of generalized multisets obtained in finitely supported mathematics where only finitely supported objects are allowed, and those obtained in the classical Zermelo-Fraenkel framework.

Keywords

MSC

03B15, 03E30, 20A10, 20E05

Cite this article

@article{cai-539,
  author  = {Andrei Alexandru and Gabriel Ciobanu},
  title   = {Generalized Multisets: From ZF to FSM},
  journal = {Computing and Informatics},
  volume  = {34},
  number  = {5},
  pages   = {1133--1150},
  year    = {2015},
  issn    = {1335-9150},
  url     = {https://cai.type.sk/content/2015/5/generalized-multisets-from-zf-to-fsm/}
}
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