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
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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 -