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A system of axiomatic set theory. Part V. General set theory (continued)

1943
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Journal of Symbolic Logic (JSL)
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We have still to consider the extension of the methods of number theory to infinite ordinals—or to transfinite numbers as they may also, as usual, be called. The means for establishing number theory are, as we know, recursive definition, complete induction, and the "principle of the least number." The last of these applies to arbitrary ordinals as well as to finite ordinals, since every nonempty class of ordinals has a lowest element. Hence immediately results also the following generalization

doi:10.2307/2271051
fatcat:ueag4c53urhg3mnavo7dg7lpuq