Full Idea
If axioms are formulated for a language (such as set theory) that lacks names for all objects, then they require the use of a satisfaction relation rather than a unary truth predicate.
Gist of Idea
If a language cannot name all objects, then satisfaction must be used, instead of unary truth
Source
Halbach,V/Leigh,G.E. (Axiomatic Theories of Truth (2013 ver) [2013], 3.3)
Book Reference
'Stanford Online Encyclopaedia of Philosophy', ed/tr. Stanford University [plato.stanford.edu], p.7
A Reaction
I take it this is an important idea for understanding why Tarski developed his account of truth based on satisfaction.