In this paper we investigate the problems of disjunctive programming with an infinite array of components forming a feasible set (as their union). The investigation continues the theme of the author's earlier work and describes an original conceptual approach to a) the analysis of saddle point problems for disjunctive Lagrangian functions, b) the analysis of dual relations for disjunctive programming problems and c) the technique of equivalent (on argument) reduction of such problems of unconstrained optimization.