Zermelo-Fraenkel set theory with choice (ZFC)
GPTKB entity
Statements (53)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
set theory
|
| gptkbp:developedBy |
gptkb:Ernst_Zermelo
gptkb:Abraham_Fraenkel |
| gptkbp:hasInfluenceOn |
category theory
modern mathematics model theory proof theory set-theoretic topology |
| gptkbp:hasRelatedPatent |
theoretical physics
computer science philosophy |
| gptkbp:hasSpecialty |
consistency
completeness decidability |
| https://www.w3.org/2000/01/rdf-schema#label |
Zermelo-Fraenkel set theory with choice (ZFC)
|
| gptkbp:includes |
Axiom of Union
Axiom of Choice Axiom of Infinity Axiom of Power Set Axiom_of_Extensionality Axiom_of_Pairing Axiom_of_Replacement |
| gptkbp:isA |
formal system
|
| gptkbp:isAssociatedWith |
gptkb:Burali-Forti_paradox
gptkb:Russell's_paradox gptkb:Cantor's_paradox gptkb:Cantor's_theorem set-theoretic paradoxes |
| gptkbp:isBasedOn |
axiomatic set theory
|
| gptkbp:isCriticizedFor |
intuitionism
constructivism finitism |
| gptkbp:isEquippedWith |
gptkb:Constructible_universe_(L)
Von_Neumann-Bernays-Gödel_set_theory_(NBG) |
| gptkbp:isExaminedBy |
educational resources
historical studies mathematical literature philosophical literature |
| gptkbp:isInformedBy |
first-order logic
axiomatic systems predicate logic |
| gptkbp:isRelatedTo |
gptkb:Cantor's_set_theory
gptkb:Gödel's_incompleteness_theorems Zorn's lemma Well-ordering theorem |
| gptkbp:isTaughtIn |
university courses
logic courses philosophy departments mathematics departments foundations of mathematics courses |
| gptkbp:isUsedIn |
logic
mathematics foundations of mathematics |