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Sorry, the key point is that the assertion:

"Therefore, P is not equal to NP, is true and provable in a simply consistent extension B" of B"

does not necessarily imply P \neq NP (the caveat being the B" and B stuff). I'm not really a complexity theory guy, but I would say WHP that this either

(a) does not apply to the most general forms of computation (e.g., what people mean when they ask P =? NP)

(b) is wrong

"arXiv == not peer reviewed."

Although amusingly, I heard that Cornell was sued for not allowing creationists to post their physics theories there.

His homepage is amusingly antiquated, even for an academic.

I think "minimal" is the preferred term.

Perhaps, but antiquated probably applies given that he has yahoo listed in his "hot links"