Positive Topology and Feasible Refinement: Forcing Matrices, Positivity, and Information

תקציר מקורי באנגליתarXiv:2609.13523v1 Announce Type: cross Abstract: We develop a conceptual and operational account of Positive Topology starting from a basic relation between points or models and observable properties. From this relation, two complementary structures emerge. The first captures universal refinement and cover: what must hold across all relevant cases and how information can be systematically refined. The second captures positivity and witnessed existence: what can be positively realized and sustained without relying on classical complements. A central result shows that the underlying relation between points and observables can be reconstructed from either of these induced structures. We also clarify the distinction between point-based and pointfree formulations: when points are available, po