Thanks for explaining this, it truly is fascinating. This appears to be an argument that almost every axiomatic theory isn't Σ₁-sound. So I can only ask a few

Thanks for explaining this, it truly is fascinating. This appears to be an argument that almost every axiomatic theory isn't Σ₁-sound. So I can only ask a few things: 1. How do I even learn about Σ₁-soundness? I've tried for 30 minutes now to search for it. 2. Is my impression correct? Does this argument show that for ex ZFC is not Σ₁-sound? If not, which axiomatic theories exactly fall into this trap?