150 research outputs found
The Complexity of Orbits of Computably Enumerable Sets
The goal of this paper is to announce there is a single orbit of the c.e.
sets with inclusion, \E, such that the question of membership in this orbit
is -complete. This result and proof have a number of nice
corollaries: the Scott rank of \E is \wock +1; not all orbits are
elementarily definable; there is no arithmetic description of all orbits of
\E; for all finite , there is a properly
orbit (from the proof).
A few small corrections made in this versionComment: To appear in the Bulletion of Symbolic Logi
Newcomb's Paradox: a Subversive Interpretation
A re-interpretation of the asymmetric roles assigned to the two agents in the genesis of Newcombâs Paradox is suggested. The re-interpretation assigns a more active role for the 'rational' agent and a possible Turing Machine interpretation for the behaviour of the demon (alias 'being from another planet, with an advanced technology and science,..,etc.'). These modifications, while introducing new conundrums to an already diabolical interaction, do allow the 'rational' agent, as a computably behavioural agent, to make a clear decision, if any decision is possible at all. This latter caveat is necessary because in the Turing Machine formulation, the computably behavioural agent might have to face algorithmic undecidabilities
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