Full Idea
The global reflection principle ∀x(Sent(x) ∧ Bew[PA](x) → Tx) …seems to be the full statement of the soundness claim for Peano arithmetic, as it expresses that all theorems of Peano arithmetic are true.
Clarification
Bew[PA] means provable in Peano arithmetic. T means 'true'
Gist of Idea
The global reflection principle seems to express the soundness of Peano Arithmetic
Source
Volker Halbach (Axiomatic Theories of Truth [2011], 22.1)
Book Reference
Halbach,Volker: 'Axiomatic Theories of Truth' [CUP 2011], p.323
A Reaction
That is, an extra principle must be introduced to express the soundness. PA is, of course, not complete.
Related Idea
Idea 16342 You cannot just say all of Peano arithmetic is true, as 'true' isn't part of the system [Halbach]