TY - GEN

T1 - Categories of elementary sets over algebras and categories of elementary algebraic knowledge

AU - Plotkin, Boris

AU - Plotkin, Tatjana

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=49949087676&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-78127-1_30

DO - 10.1007/978-3-540-78127-1_30

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:49949087676

SN - 3540781269

SN - 9783540781264

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 555

EP - 570

BT - Pillars of Computer Science - Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday

A2 - Avron, Arnon

A2 - Dershowitz, Nachum

A2 - Rabinovich, Alexander

ER -