The present article extends the 0-1 law upon the class of ℒ₀ language extension class that are dubbed iterative extensions. We introduce the notion of extended language formula approximation by first-order formulas. The problem of computing a limit value for the proportion of satisfiable formulas in iterative extensions is reduced to the computation of the limit for the proportion of satisfiable formulas among its approximations. This is illustrated by the connectivity property for graphs and some of its generalizations.

mathematical logic, iterative extensions of logic, formula approximation

Mathematical problems and theory of numerical methods