Dimensions, matroids, and dense pairs of first-order structures

Antongiulio Fornasiero

A structure M is pregeometric if the algebraic closure is a pregeometry in all structures elementarily equivalent to M. We define a generalisation: structures with an existential matroid. The main examples are superstable groups of Lascar U-rank a power of and d-minimal expansion of fields. Ultraproducts of pregeometric structures expanding an integral domain, while not pregeometric in general, do have a unique existential matroid.

Mots clés: primary; secondary; Geometric structure; Pregeometry; Matroid; Lovely pair; Dense pair

Domaines: Logique [math.LO]

Antongiulio Fornasiero. Dimensions, matroids, and dense pairs of first-order structures. Annals of Pure and Applied Logic, 2011, 162 (7), pp.514. ⟨10.1016/j.apal.2011.01.003⟩. ⟨hal-00733120⟩