Can we instead do “probability distribution over equivalence classes of models of L”, where equivalence is determined by agreement on the truth-values of all first order sentences? There’s only 2^ℵ₀ of those, and the paper never depends on any distinction within such an equivalence class.
Can we instead do “probability distribution over equivalence classes of models of L”, where equivalence is determined by agreement on the truth-values of all first order sentences? There’s only 2^ℵ₀ of those, and the paper never depends on any distinction within such an equivalence class.
Yes, though we should just call it a “probability distribution over complete consistent theories” in that case (it’s exactly the same).