Extremal subsystems of monotonic systems

A general theoretic model is described which is intended for the initial analysis of systems of interrelated elements. In the framework of the model the existence of a special kind of subsystems called kernels is insured with monoteneity of the systems postulated. A number of extremal properties are established and the structure of the kernels is found. The language for description of such systems is described in set theoretic terms and leads to a system of notions for systems with a finite number of elements. A number of properties of special finite sequences of elements are studied whereby the kernels are identified in monotonic systems.