Mathematics · Foundations & Logic
A topic within Foundations & Logic, itself one of 13 topics in that field and part of Mathematics.
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Set Theory
Joan Bagaria · 2014
Surveys the Zermelo-Fraenkel axioms, cardinal and ordinal arithmetic, and the independence results that followed Cohen's forcing, arguing set theory…
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Contributions to the Founding of the Theory of Transfinite Numbers
Georg Cantor · 1895
Develops an arithmetic of transfinite cardinal and ordinal numbers and proves, via the diagonal argument, that some infinities are strictly larger…
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Joan Bagaria
Surveys the Zermelo-Fraenkel axioms, cardinal and ordinal arithmetic, and the independence results that followed Cohen's forcing, arguing set theory now studies the limits of its own methods as much as it studies sets.
link checked 17 Sept 2026Georg Cantor
Develops an arithmetic of transfinite cardinal and ordinal numbers and proves, via the diagonal argument, that some infinities are strictly larger than others.
link checked 17 Sept 2026Paul J. Cohen
Introduces the method of forcing to build a model of set theory in which the continuum hypothesis fails, proving it cannot be derived from the standard axioms.
link checked 17 Sept 2026