Zermelo–Fraenkel Set Theory

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:set_theory
gptkbp:abbreviation	gptkb:ZF gptkb:ZFC
gptkbp:category	gptkb:logic gptkb:set_theory
gptkbp:consistency	undecidable within ZF
gptkbp:extendedForm	gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice
gptkbp:field	gptkb:mathematics gptkb:set_theory
gptkbp:formedBy	early 20th century
gptkbp:hasModel	gptkb:constructible_universe cumulative hierarchy
https://www.w3.org/2000/01/rdf-schema#label	Zermelo–Fraenkel Set Theory
gptkbp:independenceResults	gptkb:continuum_hypothesis axiom of choice
gptkbp:influenced	gptkb:logic gptkb:category_theory foundations of mathematics model theory modern mathematics
gptkbp:influencedBy	gptkb:naive_set_theory
gptkbp:language	gptkb:first-order_logic
gptkbp:mainAxioms	gptkb:axiom_schema_of_replacement gptkb:axiom_of_foundation gptkb:axiom_of_empty_set gptkb:axiom_of_extensionality gptkb:axiom_of_pairing gptkb:axiom_of_power_set gptkb:axiom_of_regularity gptkb:axiom_of_union gptkb:axiom_schema_of_separation axiom of infinity axiom of choice (in ZFC)
gptkbp:namedAfter	gptkb:Ernst_Zermelo gptkb:Abraham_Fraenkel
gptkbp:notableFigure	gptkb:Ernst_Zermelo gptkb:John_von_Neumann gptkb:Thoralf_Skolem gptkb:Abraham_Fraenkel
gptkbp:publicationYear	1908
gptkbp:relatedTo	gptkb:Russell's_paradox gptkb:von_Neumann–Bernays–Gödel_set_theory gptkb:Morse–Kelley_set_theory axiom of choice
gptkbp:usedFor	foundation of mathematics avoiding paradoxes in naive set theory study of sets
gptkbp:bfsParent	gptkb:Axiom_Schema_of_Subsets
gptkbp:bfsLayer	8