Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
set-theoretic universe
|
| gptkbp:alsoKnownAs |
cumulative hierarchy
|
| gptkbp:basisFor |
gptkb:Zermelo-Fraenkel_set_theory
|
| gptkbp:contains |
all pure sets
|
| gptkbp:definedIn |
transfinite recursion
|
| gptkbp:describes |
hierarchy of sets
|
| https://www.w3.org/2000/01/rdf-schema#label |
Von Neumann universe
|
| gptkbp:importantFor |
gptkb:logic
gptkb:set_theory model theory |
| gptkbp:level |
V_alpha
|
| gptkbp:namedAfter |
gptkb:John_von_Neumann
|
| gptkbp:relatedTo |
gptkb:Grothendieck_universe
cumulative hierarchy |
| gptkbp:symbol |
V
|
| gptkbp:unionOf |
V_alpha for all ordinals alpha
|
| gptkbp:usedIn |
gptkb:mathematics
gptkb:set_theory |
| gptkbp:V_0 |
empty set
|
| gptkbp:V_lambda_(limit_ordinal) |
union of V_beta for beta < lambda
|
| gptkbp:V_{alpha+1} |
power set of V_alpha
|
| gptkbp:bfsParent |
gptkb:constructible_universe
gptkb:MK_set_theory gptkb:Cumulative_hierarchy |
| gptkbp:bfsLayer |
6
|