Nope, this is another case of confusing truth with provability. A doesn’t know B’s proof checker is correct, so I don’t think it can make that inference.
Actually, no. You confuse truth and provability for the second (third?) time. A doesn’t have a proof that B’s proof checker is correct, so it cannot deduce what you just deduced. Please please please, just try to parse any technical material associated with the topic. People have learned to avoid this particular pitfall decades ago. We have tools for that. I am using them heavily here.
Not if they will cooperate regardless of what you do. Then you can win more by defecting.
A knows B’s source code, and so it knows that B will only output a 1 if A and B output the same thing, i.e. only if A and B both output 1.
No, A doesn’t know that because it doesn’t know B’s proof checker is correct.
You really have to be triple extra careful when talking about this stuff. I’m trying to.
Yes, I see that.
Nope, this is another case of confusing truth with provability. A doesn’t know B’s proof checker is correct, so I don’t think it can make that inference.
Actually, no. You confuse truth and provability for the second (third?) time. A doesn’t have a proof that B’s proof checker is correct, so it cannot deduce what you just deduced. Please please please, just try to parse any technical material associated with the topic. People have learned to avoid this particular pitfall decades ago. We have tools for that. I am using them heavily here.