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gptkbp:instanceOf
|
gptkb:set_theory
|
|
gptkbp:abbreviation
|
gptkb:ZFC
|
|
gptkbp:allows
|
mathematical community
|
|
gptkbp:basisFor
|
gptkb:algebra
gptkb:geometry
gptkb:logic
gptkb:topology
gptkb:category_theory
gptkb:set-theoretic_topology
analysis
functional analysis
measure theory
model theory
number theory
combinatorics
mathematical foundations
mathematical logic research
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|
gptkbp:distinctFrom
|
gptkb:ZF_(Zermelo–Fraenkel_set_theory_without_choice)
|
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gptkbp:field
|
gptkb:mathematics
|
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gptkbp:formedBy
|
early 20th century
|
|
gptkbp:fullName
|
gptkb:Zermelo–Fraenkel_set_theory_with_the_axiom_of_choice
|
|
gptkbp:hasAxiom
|
gptkb:set_theory
gptkb:Axiom_of_Choice
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:hasModel
|
gptkb:constructible_universe_(L)
cumulative hierarchy
|
|
gptkbp:hasSubgroup
|
gptkb:Zermelo–Fraenkel_set_theory_(ZF)
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
ZFC (with choice)
|
|
gptkbp:isConsistentIf
|
ZFC is consistent if and only if no contradiction can be derived from its axioms
|
|
gptkbp:isFoundationFor
|
most of modern mathematics
|
|
gptkbp:isIncomplete
|
true
|
|
gptkbp:isUndecidable
|
true
|
|
gptkbp:proposedBy
|
gptkb:Ernst_Zermelo
gptkb:Thoralf_Skolem
gptkb:Abraham_Fraenkel
|
|
gptkbp:relatedTo
|
gptkb:Gödel's_incompleteness_theorems
gptkb:Morse–Kelley_set_theory
gptkb:Continuum_Hypothesis
gptkb:Von_Neumann–Bernays–Gödel_set_theory
gptkb:Axiom_of_Determinacy
|
|
gptkbp:usedIn
|
gptkb:set_theory
foundations of mathematics
|
|
gptkbp:bfsParent
|
gptkb:Zermelo–Fraenkel_set_theory
|
|
gptkbp:bfsLayer
|
5
|