Abstract
The theory of ordinal numbers is essentially a theory of well ordered sets. For Cantor an ordinal number was “the general concept which results from (a well-ordered aggregate) M if we abstract from the nature of its elements while retaining their order of precedence ...” It was Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970), working independently, who removed Cantor’s numbers from the realm of psychology. In 1903 Russell defined an ordinal number to be an equivalence class of well ordered sets under order isomorphism.
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© 1971 Springer-Verlag Berlin Heidelberg
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Takeuti, G., Zaring, W.M. (1971). Ordinal Numbers. In: Introduction to Axiomatic Set Theory. Graduate Texts in Mathematics, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9915-5_7
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DOI: https://doi.org/10.1007/978-1-4684-9915-5_7
Publisher Name: Springer, New York, NY
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