Abstract
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.
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Plotkin, B., Plotkin, T. (2008). Categories of Elementary Sets over Algebras and Categories of Elementary Algebraic Knowledge. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds) Pillars of Computer Science. Lecture Notes in Computer Science, vol 4800. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78127-1_30
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DOI: https://doi.org/10.1007/978-3-540-78127-1_30
Publisher Name: Springer, Berlin, Heidelberg
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