Noncommutative geometry and a discretized version of Kaluza-Klein theory with a finite field content

We consider a four-dimensional space-time supplemented by two discrete points assigned to a Z(2)-algebraic structure and develop the formalism of noncommutative geometry. By setting up a generalized vielbein, we study the metric structure. Metric-compatible torsion-free connection defines a unique finite field content in the model and leads to a discretized version of Kaluza-Klein theory. We study some special cases of this model that illustrate the rich and complex structure with massive modes and the possible presence of a cosmological constant.