Can we conclude that Peano's axioms consistent from soundness?

Question

One of the corollaries of soundness says that if $\Gamma$ is satisfiable, then $\Gamma$ is consistent. I am wondering whether we can conclude that Peano's axioms $\mathsf{PA}$ is consistent from the fact that the standard model of arithmetic $\mathcal{M}_A=(\mathbb N, 0^{\mathcal{M}_A}, s^{\mathcal{M}_A}, +^{\mathcal{M}_A}, \times^{\mathcal{M}_A}, <^{\mathcal{M}_A})$ satisfies $\mathsf{PA}$? Perhaps not?

Answer 1

Yes, absolutely. It is a theorem that $\mathsf{PA}$ is consistent. The easiest way to prove this theorem is to exhibit $\mathbb{N}$ as a model of $\mathsf{PA}$.