Abstract: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 $2 \leq k < n$); generalised $n$-gons (for $n \geq 3$); $k$-nets (for $k \geq 3$); affine planes; projective Möbius, Laguerre and Minkowski planes.
From: Davide Emilio Quadrellaro [view email]
[v1]
Sat, 16 Nov 2024 12:47:40 UTC (69 KB)
[v2]
Mon, 2 Dec 2024 11:20:46 UTC (70 KB)
[v3]
Thu, 25 Jun 2026 09:02:36 UTC (72 KB)
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