2013/09/22 by Jean Berthet, Berthet, Jean
Mathematics · #14A99 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1309.5572
openalex publication_date 2013/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several connections between finitely presented rings and ultraproducts, affine varieties and definable sets, and we introduce the key notion of an arithmetic theory as a purely algebraic version of coherent logic for rings.