Open Access
2014 A Single-Sorted Theory of Multisets
Hoang-Vu Dang
Notre Dame J. Formal Logic 55(3): 299-332 (2014). DOI: 10.1215/00294527-2688042


An axiomatic account of multiset theory is given, where multiplicities are of the same sort as sets (with their own internal structures). Various theories are proposed covering different existing multiset systems, as well as a stronger theory which is equiconsistent with Zermelo–Fraenkel set theory and with antifoundation. The inclusion relation receives a recursive definition in terms of membership and is shown to be not always antisymmetric.


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Hoang-Vu Dang. "A Single-Sorted Theory of Multisets." Notre Dame J. Formal Logic 55 (3) 299 - 332, 2014.


Published: 2014
First available in Project Euclid: 22 July 2014

zbMATH: 1337.03081
MathSciNet: MR3263530
Digital Object Identifier: 10.1215/00294527-2688042

Primary: 03E75

Keywords: antifoundation , axiomatic , multiset

Rights: Copyright © 2014 University of Notre Dame

Vol.55 • No. 3 • 2014
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