Last Updated：2025/11/24

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(set theory) The paradox that supposing the existence of a set of all ordinal numbers leads to a contradiction; construed as meaning that it is not a properly defined set.

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Burali-Forti paradox

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Burali-Forti paradox

Proper noun

(set theory) The paradox that supposing the existence of a set of all ordinal numbers leads to a contradiction; construed as meaning that it is not a properly defined set.

Japanese Meaning

（集合論）全順序数の集合が存在すると仮定することで矛盾に陥るパラドックス。これはその全順序数の集合が適切に定義された集合ではないことを意味する。

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Google Translation / DeepL Translation

講義で教授は、順序数全体の集合が存在すると仮定すると矛盾が生じるという集合論上の逆理を用いて、そのような集合が存在し得ない理由を説明した。

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(set theory) The paradox that supposing the existence of a set of all ordinal numbers leads to a contradiction; construed as meaning that it is not a properly defined set.

Like them, Mirimanoff concentrates on the Burali-Forti paradox, and like Russell's analysis before, Mirimanoff shows how. in terms of size, the Burali-Forti paradox is basic and that if we solve this the other paradoxes will be solved too.

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the Burali-Forti paradox

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Burali-Forti paradox

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