ALGEBRAIC LOGIC AND LOGICALLY-GEOMETRIC TYPES IN VARIETIES OF ALGEBRAS

作者：Plotkin Boris^*; Aladova Elena; Plotkin Eugene

来源：Journal of Algebra and Its Applications, 2013, 12(2): 1250146.

DOI：10.1142/S0219498812501460

• Model theoretic type
• logically geometric type
• isotypic algebras
• logical kernel of a point
• elementary (definable) set
• Galois correspondence
• variety of algebras

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.

• 出版日期2013-3