The Definability of Cardinal Numbers

Azriel Lévy

A chapter in Foundations of Mathematics, 1969, pp 15-38 from Springer

Abstract: Abstract One says that the sets x and y are equinumerous (in symbols, x ≈ y) if there is a 1 – 1 function mapping x on y. The notion of the cardinal |x| of x is obtained from equinumerosity by abstraction. The use of |x| does usually not require any special apparatus. E.g., when we say |x| — ℵ0 we mean to say that there is a 1 – 1 function mapping x on the set of all natural numbers; when we say |x|

Keywords: Free Variable; Cardinal Number; Axiom Schema; Operation Symbol; Membership Relation (search for similar items in EconPapers)
Date: 1969
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DOI: 10.1007/978-3-642-86745-3_3

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