Full Idea
A set of axioms is said to be ω-incomplete if, for some universal quantification, each of its instances is derivable from those axioms but the quantification is not thus derivable.
Gist of Idea
Axioms are ω-incomplete if the instances are all derivable, but the universal quantification isn't
Source
Engelbretsen,G/Sayward,C (Philosophical Logic: Intro to Advanced Topics [2011], 7)
Book Reference
Engelbretsen,G/Sayward,C: 'Philosophical Logic: Intro to Advanced Topics' [Continuum 2011], p.132