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gptkbp:instanceOf
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gptkb:mathematical_concept
set-theoretic universe
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gptkbp:axiomOfChoice
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can be true in V
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gptkbp:axiomOfEmptySet
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true in V
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gptkbp:axiomOfExtensionality
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true in V
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gptkbp:axiomOfFoundation
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true in V
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gptkbp:axiomOfInfinity
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true in V
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gptkbp:axiomOfPairing
|
true in V
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gptkbp:axiomOfPowerSet
|
true in V
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gptkbp:axiomOfRegularity
|
true in V
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gptkbp:axiomOfReplacement
|
true in V
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gptkbp:axiomOfSeparation
|
true in V
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gptkbp:axiomOfUnion
|
true in V
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gptkbp:basisFor
|
gptkb:set_theory
|
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gptkbp:builtBy
|
cumulative hierarchy
transfinite recursion
|
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gptkbp:category
|
gptkb:set_theory
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gptkbp:contains
|
all sets
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gptkbp:definedIn
|
gptkb:John_von_Neumann
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Von Neumann universe (V)
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gptkbp:level
|
V_alpha
V_0 = empty set
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gptkbp:limitLevel
|
V_lambda = union of V_beta for beta < lambda
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gptkbp:namedAfter
|
gptkb:John_von_Neumann
|
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gptkbp:relatedTo
|
gptkb:Grothendieck_universe
gptkb:constructible_universe_(L)
|
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gptkbp:successorLevel
|
V_{alpha+1} = P(V_alpha)
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gptkbp:symbol
|
V
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gptkbp:unionOf
|
V_alpha for all ordinals alpha
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gptkbp:usedIn
|
gptkb:Zermelo–Fraenkel_set_theory
gptkb:set_theory
|
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gptkbp:bfsParent
|
gptkb:constructible_universe_(L)
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gptkbp:bfsLayer
|
7
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