Algebraic logic and logically-geometric types in varieties of algebras

Details Algebraic logic and logically-geometric types in varieties of algebras Algebraic logic and logically-geometric types in varieties of algebras

2011-08-02

arxiv.org/abs/1108.0573v1

Mathematics

Logic

Scientific paper

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.

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