Statements (20)
Predicate | Object |
---|---|
gptkbp:instanceOf |
gptkb:Titan
set theory principle |
gptkbp:allows |
most mathematicians
|
gptkbp:equivalentTo |
every countable product of non-empty sets is non-empty (in ZF)
|
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:introducedIn |
1904
|
gptkbp:isWeakerThan |
gptkb:axiom_of_dependent_choice
axiom of choice |
gptkbp:notProvableIn |
ZF (Zermelo-Fraenkel set theory without choice)
|
gptkbp:opposedBy |
constructivist mathematicians
|
gptkbp:statedIn |
For any countable collection of non-empty sets, there exists a choice function selecting one element from each set.
|
gptkbp:symbol |
AC_ω
|
gptkbp:usedIn |
gptkb:topology
analysis functional analysis |
gptkbp:bfsParent |
gptkb:countable_axiom_of_choice
gptkb:Zermelo’s_Axiom_of_Choice |
gptkbp:bfsLayer |
8
|