Suppose that $\varphi$ is a consequence of every standard model of PA. Then is it provable from PA?
2026-03-25 16:03:22.1774454602
If a statement holds for all standard models of PA, then does it hold for all models?
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There is (up to isomorphism) only one standard model of PA. And there are sentences true in the natural numbers that are not theorems of PA.