Algebraic logic and logically-geometric types in varieties of algebras

Boris Plotkin; Elena Aladova; Eugene Plotkin

doi:10.1142/S0219498812501460

Algebraic logic and logically-geometric types in varieties of algebras

Boris Plotkin
, Elena Aladova
, Eugene Plotkin

Department of Mathematics

Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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.

Original language	English
Article number	1250146
Journal	Journal of Algebra and its Applications
Volume	12
Issue number	2
DOIs	https://doi.org/10.1142/S0219498812501460
State	Published - Mar 2013

Bibliographical note

Funding Information:
E. Aladova was supported by the Minerva foundation through the Emmy Noether Research Institute, by the Israel Science Foundation and ISF center of excellence 1691/10. The support of these institutions is gratefully appreciated. E. Plotkin is thankful for the support of the Minerva foundation through the Emmy Noether Research Institute.

Funding

E. Aladova was supported by the Minerva foundation through the Emmy Noether Research Institute, by the Israel Science Foundation and ISF center of excellence 1691/10. The support of these institutions is gratefully appreciated. E. Plotkin is thankful for the support of the Minerva foundation through the Emmy Noether Research Institute.

Funders	Funder number
Emmy Noether Research Institute for Mathematics
Minerva Foundation
Israel Science Foundation	1691/10

Keywords

Galois correspondence
Model theoretic type
elementary (definable) set
isotypic algebras
logical kernel of a point
logically geometric type
variety of algebras

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10.1142/S0219498812501460

Cite this

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Algebraic logic and logically-geometric types in varieties of algebras

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Keywords

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