In set theory, a field of mathematics, the Burali-Forti paradox demonstrates that constructing "the set of all ordinal numbers" leads to a contradiction...

inconsistent. Prior to Russell's paradox (and to other similar paradoxes discovered around the time, such as the Burali-Forti paradox), a common conception of...

After the discovery of paradoxes within naive set theory (such as Russell's paradox, Cantor's paradox and the Burali-Forti paradox), various axiomatic systems...

ordinal numbers cannot logically exist seems paradoxical to many. This is related to the Burali-Forti's paradox which implies that there can be no greatest...

conversely, the latter statement implies Cantor's paradox. By applying this indexing to the Burali-Forti paradox we obtain another proof that the cardinal numbers...

liar paradox, Socratic paradox and the Burali-Forti paradox, all of which have self-reference in common with Epimenides. The Epimenides paradox is usually...

Cesare Burali-Forti (13 August 1861 – 21 January 1931) was an Italian mathematician, after whom the Burali-Forti paradox is named. He was a prolific writer...

is a set is not only Cantorian set but strongly Cantorian. The Burali-Forti paradox of the largest ordinal number is resolved in the opposite way: In...

completely, however, lecturing on the paradoxes of set theory (Burali-Forti paradox, Cantor's paradox, and Russell's paradox) to a meeting of the Deutsche...

(where it affords a rather surprising alternative solution to the Burali-Forti paradox of the largest ordinal). Rather than defining an ordinal as an equivalence...

ZFC is immune to the classic paradoxes of naive set theory: Russell's paradox, the Burali-Forti paradox, and Cantor's paradox. Abian & LaMacchia (1978) studied...

themselves is proper, and the Burali-Forti paradox suggests that the class of all ordinal numbers is proper. The paradoxes do not arise with classes because...

some of the paradoxes following from unrestricted interpretation of his theory, for instance Cantor's paradox and the Burali-Forti paradox, and did not...

Reinhold. Mirimanoff, Dmitry (1917). "Les antinomies de Russell et de Burali-Forti et le probleme fondamental de la theorie des ensembles". L'Enseignement...

instead. Burali-Forti paradox: If the ordinal numbers formed a set, it would be an ordinal number that is smaller than itself. Cantor's paradox: The set...

same size as the part.[citation needed] One example of this is Hilbert's paradox of the Grand Hotel. Indeed, Dedekind defined an infinite set as one that...

predicate is true. This can easily lead to contradictions and paradoxes. For example, Russell's paradox shows that the expression { x   |   x ∉ x } , {\displaystyle...

Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg Cantor...

Lebesgue-measure σ-algebra on the real numbers. The Hausdorff paradox. The Banach–Tarski paradox. Algebra Every field has an algebraic closure. Every field...

Boolean-valued model Burali-Forti paradox Cantor's back-and-forth method Cantor's diagonal argument Cantor's first uncountability proof Cantor's paradox Cantor's...

A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently...

R_{U}.} This argument is known as Russell's paradox. As a point of subtlety, the version of Russell's paradox we have presented here is actually a theorem...

discussed below. Because restricting comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Gödel considered...

propose to be talking about. In 1897 the Italian mathematician Cesare Burali-Forti discovered that there is no set containing all ordinal numbers. As every...

Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg Cantor...

function, but a function-like class, as it is not a set (due to the Burali-Forti paradox). For any ordinal α we have α ≤ ωα. In many cases ωα is strictly...

recently discovered paradoxes in naive set theory. Cesare Burali-Forti was the first to state a paradox: the Burali-Forti paradox shows that the collection...

useful in mathematics, but paradoxes arise if no restrictions are placed on how sets can be constructed: Russell's paradox shows that the "set of all...

; Nelson, L. (1908). "Bemerkungen zu den Paradoxien von Russell und Burali-Forti". Abhandlungen der Fries'schen Schule II. Göttingen. pp. 301–334.{{cite...

Morse–Kelley Kripke–Platek Tarski–Grothendieck Paradoxes Problems Russell's paradox Suslin's problem Burali-Forti paradox Set theorists Paul Bernays Georg Cantor...