[FOM] Absolute undecidability

[Arne Hole]

Last autumn, I posted the message cited below to FOM concerning my project on absolute undecidability. Since then, I have become aware of some (known) results on incompressibility making it possible to carry this much further. On my draft sharing page 

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

you will find the current version of my paper. You will also find a PP presentation aimed at getting the main point across in the simplest way possible. You get directly to the PP at

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

As before, comments are very welcome. 
Best wishes, Arne H.


>-----Original Message-----
>From: Arne Hole
>Sent: Monday, September 07, 2015 1:26 PM
>To: 'fom at cs.nyu.edu'
>Subject: Absolute undecidability
>
>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.