Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Titan
gptkb: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
|
| 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:analysis
gptkb:topology functional analysis |
| gptkbp:bfsParent |
gptkb:countable_axiom_of_choice
gptkb:Zermelo’s_Axiom_of_Choice |
| gptkbp:bfsLayer |
8
|
| https://www.w3.org/2000/01/rdf-schema#label |
axiom of countable choice
|