Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
Set theory principle |
| gptkbp:allows |
Most mathematicians
|
| gptkbp:distinctFrom |
gptkb:Axiom_of_Choice
|
| gptkbp:equivalentTo |
Every countable product of non-empty sets is non-empty (in ZF)
|
| gptkbp:field |
gptkb:Mathematics
gptkb:Set_theory |
| gptkbp:firstAppearance |
20th century
|
| gptkbp:formedBy |
gptkb:Ernst_Zermelo
|
| https://www.w3.org/2000/01/rdf-schema#label |
Axiom of Countable Choice
|
| gptkbp:implies |
Axiom of Countable Union
|
| gptkbp:isWeakerThan |
gptkb:Axiom_of_Choice
gptkb:Axiom_of_Dependent_Choice |
| gptkbp:relatedTo |
gptkb:Axiom_of_Choice
gptkb:Axiom_of_Dependent_Choice |
| gptkbp:statedIn |
Every countable family of non-empty sets has a choice function.
|
| gptkbp:status |
Independent of Zermelo–Fraenkel set theory (ZF)
|
| gptkbp:symbol |
AC_ω
|
| gptkbp:usedIn |
gptkb:Topology
Analysis Functional analysis |
| gptkbp:bfsParent |
gptkb:Axiom_of_Choice_(AC)
|
| gptkbp:bfsLayer |
8
|