Full Idea
Combinatorial collections (defined just by the members) obviously obey the Axiom of Choice, while it is at best dubious whether logical connections (defined by a rule) do.
Gist of Idea
Pure collections of things obey Choice, but collections defined by a rule may not
Source
Shaughan Lavine (Understanding the Infinite [1994], IV.2)
Book Reference
Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.78