Asymptotic densities in logic and type theory (Q931404)

The authors investigate the proportion between the number of valid propositional formulae of a given length \(n\) against the number of all formulae of length \(n\). The particular interest is to find the limit, if it exists, of the fraction when \(n\to\infty\), represented by a real number called the density of truth of the considered logic. A short review of the authors' earlier extremely interesting results has been presented [see Stud. Log. 76, No. 3, 307--328 (2004; Zbl 1049.03007)] and, in the sequel, it has been proved that the probability of randomly chosen fourth-order type admitting decidable lambda definability problem is zero.