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We prove that any equational basis that defines representable relation algebras (RRA) over weakly representable relation algebras (wRRA) must contain infinitely many variables. The proof uses a construction of arbitrarily large finite weakly representable but not representable relation algebras whose “small” subalgebras are representable. [ABSTRACT FROM AUTHOR]

We give a simple new construction of representable relation algebras with non-representable completions. Using variations on our construction, we show that the elementary closure of the class of completely representable relation algebras is not finitely axiomatizable (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We investigate the complexity of the typability problem for the relational algebra. This problem consists of deciding, for a given relational algebra expression, whether there exists an assignment of types to variables occurring in the expression such that the expression is well-typed under the assignment. We obtain that the problem is NP-complete in general. In particular, we show that the problem becomes NP-hard due to (1) the cartesian product operator, (2) the selection operator on arbitrary sets of typed predicates, (3) the selection operator on “well-behaved” sets of typed predicates together with join and projection or renaming. However, the problem is in P when (1) we only allow union, difference, join and selection on “well-behaved” sets of typed predicates, or (2) we allow all operators except cartesian product, where the set of selection predicates can mention at most one base type. Most of these results follow from a close connection of the typability problem to non-uniform constraint satisfaction. [ABSTRACT FROM AUTHOR]

The article reports on a study published within the issue related to mathematics students' understanding of distinction between the concepts of function and relation in Greece. It examines students' awareness of the discrimination between function and relation, and the discrimination between the dependent and the independent variables. It presents results of the questionnaires and interviews that students experienced difficulties in answering them. It states that the students' examples and their application of the definition explored a constrained perception of the function concept. Therefore, in order to overcome the obstacle of confusing the function with a relation, it suggests a teaching of function oriented towards activities which demand the measure of a magnitude.