Set-theoretic Foundations of the Modern Relational Databases: Representations of Table Algebras Operations

The article is dedicated to the creation of the fragment of table algebras theory constructed on the basis of classical relational Codd’s algebras. The distinctive peculiarity of the adapted technique is the use of set-theoretic properties of some constructions (full image of the set with respect to the function, function restriction with respect to the set, generalized direct (Cartesian) product, binary relation of functions compatibility) and their transference on a case of tables. The transference of these properties is possible in view of simplicity of signature operations representations in terms of indicated set-theoretic constructions.