Single Idea 13487

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers]

Full Idea

In Zermelo's set theory, the Burali-Forti Paradox becomes a proof that there is no set of all ordinals (so 'is an ordinal' has no extension).

Gist of Idea

In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals

Source

report of Ernst Zermelo (Investigations in the Foundations of Set Theory I [1908]) by William D. Hart - The Evolution of Logic 3

Book Reference

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.70

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