2011/08/02 by B. Plotkin, Plotkin, Boris, Elena Aladova +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.1108.0573
openalex publication_date 2011/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic geometry to the model theory through the machinery of algebraic logic. We show that types appear naturally as logical kernels in the Galois correspondence between filters in the Halmos algebra of first order formulas with equalities and elementary sets in the corresponding affine space.