Zermelo–Fraenkel set theory
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"Just as liberal feminists are frequently content with a minimal agenda of legal and social equality for women and "pro-choice", so liberal (and even some socialist) mathematicians are often content to work within the hegemonic Zermelo–Fraenkel framework (which, reflecting its nineteenth-century liberal origins, already incorporates the axiom of equality) supplemented only by the axiom of choice."--"Transgressing the Boundaries: Towards a Transformative Hermeneutics of Quantum Gravity" (1996) |
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In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics. Zermelo–Fraenkel set theory with the axiom of choice included is abbreviated ZFC, where C stands for "choice",<ref>Template:Harvnb. "Zermelo-Fraenkel axioms (abbreviated as ZFC where C stands for the axiom of Choice"</ref> and ZF refers to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded.
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