Algebraic logic and logically-geometric types in varieties of algebras

Boris Plotkin, Elena Aladova, Eugene Plotkin

Research output: Contribution to journalArticlepeer-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 languageEnglish
Article number1250146
JournalJournal of Algebra and its Applications
Volume12
Issue number2
DOIs
StatePublished - 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.

FundersFunder number
Emmy Noether Research Institute
Minerva Foundation
Israel Science Foundation1691/10

    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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