Algebraic logic and logically-geometric types in varieties of algebras
Logic
2011-08-03 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1108.0573,
title = {Algebraic logic and logically-geometric types in varieties of algebras},
author = {Boris Plotkin and Elena Aladova and Eugene Plotkin},
journal= {arXiv preprint arXiv:1108.0573},
year = {2011}
}