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30 de abr. de 2024 · Teoría de conjuntos de Zermelo-Fraenkel: En respuesta a la paradoja de Russell y otras paradojas lógicas, los matemáticos Ernst Zermelo y Abraham Fraenkel desarrollaron la teoría de conjuntos de Zermelo-Fraenkel (ZF), que emplea un conjunto de axiomas que evitan la formación de conjuntos como 𝑅 R en la paradoja de Russell.
30 de abr. de 2024 · Zermelo-Fraenkel Set Theory: In response to Russell’s Paradox and other logical paradoxes, mathematicians Ernst Zermelo and Abraham Fraenkel developed Zermelo-Fraenkel set theory (ZF), which employs a set of axioms that avoid the formation of sets like 𝑅R in Russell’s Paradox.
27 de abr. de 2024 · In the same vein, Ernst Zermelo tried to axiomatize set theory. His system of axioms made it possible to save set theory from the famous Russell’s paradox, and also includes a controversial one, the axiom of choice.
1 de may. de 2024 · In 1904, Ernst Zermelo promotes axiom of choice and his proof of the well-ordering theorem. Bertrand Russell would shortly afterward introduce logical disjunction in 1906. Also in 1906, Poincaré would publish On the Dynamics of the Electron and Maurice Fréchet introduced metric space.
27 de abr. de 2024 · Part of the process of proof analysis involves the identification of hidden premises in mathematical arguments, and in particular in attempts to prove certain results. This is particularly clear in the case of Ernst Zermelo’s original axiomatization of set theory, and the resulting uncovering of the axiom of choice (Zermelo 1904/ ...
Hace 1 día · In 1913, Ernst Zermelo published Über eine Anwendung der Mengenlehre auf die Theorie des Schachspiels (On an Application of Set Theory to the Theory of the Game of Chess), which proved that the optimal chess strategy is strictly determined. This paved the way for more general theorems.
27 de abr. de 2024 · Moreover, second-order ZFC set theory enjoys what is known as quasi-categoricity. Namely, Ernst Zermelo proved that the second-order version of ZFC axioms, known as ZFC 2, has one single type of models, namely the sets V κ for a strongly inaccessible cardinal κ.
