axiom of countable choice

GPTKB entity

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