Word info

ZFC

Noun

Meaning

(set theory) Initialism of Zermelo-Fraenkel set theory with Choice; the standard axiomatization of set theory, including the axiom of choice.

(physics) Initialism of zero-field cooling; the act of cooling with no magnetic field applied

Source: en.wiktionary.org

Examples

A cardinal is defined to be an equivalence class of similar classes (as opposed to ZFC, where a cardinal is a special sort of von Neumann ordinal). Source: Internet

Additionally, this result implies that proving independence from PA or ZFC using currently known techniques is no easier than proving the existence of efficient algorithms for all problems in NP. Source: Internet

Arguments for and against CH Gödel believed that CH is false and that his proof that CH is consistent with ZFC only shows that the Zermelo–Fraenkel axioms do not adequately characterize the universe of sets. Source: Internet

Because at least one such infinite schema is required (ZFC is not finitely axiomatizable), this shows that the axiom schema of replacement can stand as the only infinite axiom schema in ZFC if desired. Source: Internet

As GCH implies CH, Cohen's model in which CH fails is a model in which GCH fails, and thus GCH is not provable from ZFC. Source: Internet

Equivalently, these statements are true in all models of ZFC but false in some models of ZF. Source: Internet

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