Numerosities of labelled sets: a new way of counting

The notions of “labelled set” and “numerosity” are introduced to generalize the counting process of finite sets. The resulting numbers, called numerosities, are then used to develop nonstandard analysis. The existence of a numerosity function is equivalent to the existence of a selective ultrafilter...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2003-01, Vol.173 (1), p.50-67
Main Authors: Benci, Vieri, Di Nasso, Mauro
Format: Article
Language:English
Subjects:
Nonstandard analysis
Other hypotheses and axioms
Ultraproducts and related constructions
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Summary:The notions of “labelled set” and “numerosity” are introduced to generalize the counting process of finite sets. The resulting numbers, called numerosities, are then used to develop nonstandard analysis. The existence of a numerosity function is equivalent to the existence of a selective ultrafilter, hence it is independent of the axioms of ZFC.
ISSN:0001-8708
1090-2082
DOI:10.1016/S0001-8708(02)00012-9