[FOM] First Order Logic/status
joeshipman at aol.com
Sun Oct 29 09:45:35 EST 2006
AX1 EX2 EX3 (X1+x2=X3 & AX4 AX5 ~(SSX4*SSX5=X3 V SS4*SS5=SSX3))
AX1 EX2 EX3 (SSX1+SSX1=X2+X3 & AX4 AX5 ~(SSX4*SSX5=X2 V SSX4*SSX5=X3))
>> ***Under any reasonable measure of complexity of sentences in the
>> of PA, any sentence or scheme in the language of PA of modest
>> either provable or refutable in PA.***
> This assertion surprises me. I for one don't believe it, and see no
> evidence for it considering the large number of such sentences that
> remained unresolved despite great interest.
Not a single one of them is of reasonable complexity as sentences or
in the primitive language of PA with 0,S,+,x.
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