2024/11/16 by Gianluca Paolini, Paolini, Gianluca, Davide Emilio Quadrellaro +1 · 2 citations
Engineering · #Evacuation and Crowd Dynamics
paper · pdf · doi:10.48550/arxiv.2411.10792
Taking inspiration from [1, 21, 24], we develop a general framework to deal with the model theory of open incidence structures. In this first paper we focus on the study of systems of points and lines (rank 2). This has a number of applications, in particular we show that for any of the following classes all the non-degenerate free structures are elementarily equivalent, and their common theory is decidable, strictly stable, and with no prime model: (k, n)-Steiner systems (for 2 ≤ k < n); generalised n-gons (for n ≥ 3); k-nets (for k ≥ 3); affine planes; projective Möbius, Laguerre and Minkowski planes.