Several different versions of the theory of numerosities have been introduced in the literature. Here, we unify these approaches in a consistent frame through the notion of set of labels, relating numerosities with the Kiesler field of Euclidean numbers. This approach allows to easily introduce, by means of numerosities, ordinals and their natural operations, as well as the Lebesgue measure as a counting measure on the reals.
Euclidean numbers and numerosities / V. Benci, L.L.B.. - In: THE JOURNAL OF SYMBOLIC LOGIC. - ISSN 0022-4812. - 89:1(2024 Mar), pp. PII S0022481222000172.112-PII S0022481222000172.146. [10.1017/jsl.2022.17]
Euclidean numbers and numerosities
L. Luperi BagliniUltimo
2024
Abstract
Several different versions of the theory of numerosities have been introduced in the literature. Here, we unify these approaches in a consistent frame through the notion of set of labels, relating numerosities with the Kiesler field of Euclidean numbers. This approach allows to easily introduce, by means of numerosities, ordinals and their natural operations, as well as the Lebesgue measure as a counting measure on the reals.
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