Limiting Decidability and Probability
Bernhard Lauth · 1995
Kevin Kelly has shown recently (drawing on earlier results that have been obtained by Putnam and Gold) that the notions of verification and falsification in the limit of an hypothesis h ⊂ ωN can be characterized by the position of the hypothesis with respect to the finite Borel hierarchy, (h is verifiable in the limit, iff it is Σ2, h is falsifiable in the limit, iff it is 2, and h is decidable in the limit, iff it is Δ2). In this paper, I will propose a stochastic version of testing in the limit, which works for hypotheses of arbitrary complexity with respect to the Borel scale.