@orthonormal: Thanks for pointing me to these posts during our dinner last Thursday.
I haven't checked the proofs in detail, and I didn't read all previous posts in the series. I'm a bit confused about a couple of things, and I'd be happy if someone could enlighten me.
1) What is the purpose of the i-loops?
In your definition of FairBot and others, you check for all i=1,...,N whether some sentence is provable in PA+i. However, if a sentence is provable in PA+i, then it is also provable in PA+(i+1). For this reason, I don't understand why you loop over i=1,...... (read more)
@orthonormal: Thanks for pointing me to these posts during our dinner last Thursday.
I haven't checked the proofs in detail, and I didn't read all previous posts in the series. I'm a bit confused about a couple of things, and I'd be happy if someone could enlighten me.
1) What is the purpose of the i-loops?
In your definition of FairBot and others, you check for all i=1,...,N whether some sentence is provable in PA+i. However, if a sentence is provable in PA+i, then it is also provable in PA+(i+1). For this reason, I don't understand why you loop over i=1,...... (read more)