This paper introduces Delta sets () as formally defined regions of non-derivability within a formal theory, establishing a precise link between logical incompleteness and the boundary-based formulations of the TNA framework. We prove that for any incomplete theory, the Delta set is non-empty and constitutes the structural boundary of the system (T =). The study demonstrates that these sets induce a partition of the domain and correspond to regions of zero derivability reliability (R=0). Furthermore, we provide a formal construction of boundary pressure (FB) derived from the magnitude and weighting of the Delta set, showing that incompleteness fundamentally generates a structural pressure for theoretical extension. This results in a formal grounding for the transition from axiomatic systems to dynamic boundary structures
Claudio Bresciano (Wed,) studied this question.