Zermelo-Fraenkel set theory

URI: https://gptkb.org/entity/Zermelo-Fraenkel_set_theory
GPTKB entity
Statements (49)
Predicate Object
gptkbp:instanceOf gptkb:set_theory
gptkbp:abbreviation gptkb:ZF
gptkbp:field gptkb:mathematics
gptkb:set_theory
gptkbp:formedBy early 20th century
gptkbp:hasAxiom gptkb:Axiom_of_Empty_Set
gptkb:Axiom_of_Extensionality
gptkb:Axiom_of_Infinity
gptkb:Axiom_of_Pairing
gptkb:Axiom_of_Power_Set
gptkb:Axiom_of_Regularity
gptkb:Axiom_of_Replacement
gptkb:Axiom_of_Separation
gptkb:Axiom_of_Union
gptkbp:hasAxiomSchema gptkb:Axiom_schema_of_replacement
gptkb:Axiom_schema_of_separation
gptkbp:hasModel gptkb:von_Neumann_universe
gptkbp:hasStandardModel hereditarily finite sets
https://www.w3.org/2000/01/rdf-schema#label Zermelo-Fraenkel set theory
gptkbp:influencedBy gptkb:Ernst_Zermelo
gptkb:Thoralf_Skolem
gptkb:Abraham_Fraenkel
gptkbp:isConsistentIf there is an inaccessible cardinal
gptkbp:isCumulativeHierarchy yes
gptkbp:isFoundationFor gptkb:logic
gptkb:set-theoretic_topology
analysis
measure theory
modern mathematics
gptkbp:isIncomplete due to Gödel's incompleteness theorems
gptkbp:isStandardFormulationOf gptkb:set_theory
gptkbp:language gptkb:first-order_logic
gptkbp:limitation cannot prove its own consistency (Gödel's incompleteness theorems)
gptkbp:namedAfter gptkb:Ernst_Zermelo
gptkb:Abraham_Fraenkel
gptkbp:oftenExtendedWith gptkb:Axiom_of_Choice
gptkbp:prevention gptkb:Russell's_paradox
gptkbp:purpose foundation for most of mathematics
gptkbp:relatedTo gptkb:set_theory
gptkb:Peano_axioms
gptkb:category_theory
gptkb:constructible_universe
gptkb:large_cardinal_axioms
gptkbp:replacedBy gptkb:naive_set_theory
gptkbp:usedIn gptkb:logic
foundations of mathematics
gptkbp:withAxiomOfChoice gptkb:ZFC
gptkbp:bfsParent gptkb:set_theory
gptkbp:bfsLayer 4