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The comparison principle in mathematical systems theory

A comparison principle in mathematical systems theory was derived and realized as a program in [lj -[4]; it defines algorithms for the derivation of comparison theorems giving conditions for the presence of various properties of systems in environments (similar to multibasic models). In this report the comparison principle is presented in a general form as a set of methods for solving certain logical equations in the predicate calculus (§ 1); we indicate its applications to model theory (§2) and to the analysis of properties of solutions of differential equations (§ 3) for which it has been possible to prove the necessity of the conditions of the derived comparison theorems.