[FOM] Absolute undecidability

[Arne Hole]

Earlier this summer I posted a link to a draft paper on the subject of absolute undecidability (underdetermination of truth). I have received some useful comments, but I still feel that the main point, which I think is quite significant,  has not come across. Therefore, in an attempt to make things as transparent as possible, I have now made a short PP presentation giving a simple example based on my results. You may find it at

http://folk.uio.no/arnehole/AbsUndec.pdf

This should take only some minutes to scan through. It is shown that if all closed formulas in the language L of PA are either true or false in the standard model N, then for each real number r whose base 2 decimals are definable in L, there is a closed formula A_r in L such that if we are able to decide the truth value of A_r in N, then we will have nontrivial information concerning an infinite number of decimal bits in r. As an example, I take r to be the halting probability known as Chaitin's Omega. Other interesting examples include pi, the Euler number e etc. 

Best, Arne H.