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Full Idea
Axioms specify how each unstructured predicate is satisfied by a particular sequence. Then recursive axioms characterise complex sentences built from simpler ones. Closed sentences have no free variables, so true sentences are satisfied by all sequences.
Gist of Idea
Axioms spell out sentence satisfaction. With no free variables, all sequences satisfy the truths
Source
Donald Davidson (Truth and Predication [2005], 7)
Book Ref
Davidson,Donald: 'Truth and Predication' [Belknap Harvard 2005], p.160
A Reaction
I take 'all sequences' to mean all combinations of objects in the domain. Thus nothing in domain contradicts the satisfied sentences. Hence Tarski's truth is said to be 'true in a model', where the whole system vouches for the sentence.
Related Ideas
Idea 19175 Tarski gave axioms for satisfaction, then derived its explicit definition, which led to defining truth [Tarski, by Davidson]
Idea 19191 Specify satisfaction for simple sentences, then compounds; true sentences are satisfied by all objects [Tarski]