Categories of elementary sets over algebras and categories of elementary algebraic knowledge

Boris Plotkin, Tatjana Plotkin

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

9 Scopus citations


For every variety of algebras Θ and every algebra H in Θ we consider the category of algebraic sets K Θ (H) in Θ over H. We consider also the category of elementary sets LK Θ (H). The latter category is associated with a geometrical approach to the First Order Logic over algebras. It is also related to the category of elementary knowledge about algebra H. Grounding on these categories we formally introduce and study the intuitive notions of coincidence of algebraic geometries over algebras H 1 and H 2 from Θ, of coincidence of logics over H 1 and H 2, and of coincidence of the corresponding knowledge. This paper is a survey of ideas stimulated by this approach.

Original languageEnglish
Title of host publicationPillars of Computer Science - Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday
EditorsArnon Avron, Nachum Dershowitz, Alexander Rabinovich
Number of pages16
StatePublished - 2008

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4800 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


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