Full Idea
While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models.
Gist of Idea
While true-in-a-model seems relative, true-in-all-models seems not to be
Source
E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4)
A Reaction
[The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc.
Related Ideas
Idea 10017 Truth in a model is more tractable than the general notion of truth [Hodes]
Idea 13634 Satisfaction is 'truth in a model', which is a model of 'truth' [Shapiro]