Relational model

Data are represented as database relations whose database tuples have named database attributes.

Names of database relations, their database attributes and value domains, together with applicable database integrity constraints.

A decomposition in which the database integrity constraints can be enforced using constraints on individual component database relations, without computing their relational join.

A decomposition of a relational schema whose component relational projections always reconstruct the original database relation by natural join, without extra database tuples.

A relational schema is in fourth normal form if the determinant of every non-trivial multivalued dependency is a superkey. This implies Boyce-Codd normal form because every functional dependency implies a multivalued dependency.

A relational schema is in Boyce-Codd normal form if the determinant of every non-trivial functional dependency is a superkey.

For database tuples agreeing on $X$, requires the combinations obtained by swapping their values on $Y\setminus X$ and on the remaining database attributes to occur too. A functional dependency implies the corresponding multivalued dependency; complementation exchanges $Y$ with the remaining database attributes. A multivalued dependency is trivial if $Y\subseteq X$ or $X\cup Y$ is the full relational schema.

A database integrity constraint saying that any two database tuples agreeing on database attributes $X$ also agree on database attributes $Y$.

The set of database attributes determined by $X$ under given functional dependencies. Start from $X$ and repeatedly add the right-hand side of each functional dependency whose left-hand side is already included.

A database integrity constraint requiring values of specified database attributes to occur in a referenced identifier of another database relation.

A set of database attributes that determines every database attribute of a database relation under its database integrity constraints.

An inclusion-minimal superkey: removing any of its database attributes destroys the superkey property. Minimal means inclusion-minimal, not necessarily smallest in size.

The candidate key selected as the principal identifier for database tuples of a database relation.

A condition required of every legal instance of a relational schema.

A named component of a database tuple.

One record of a database relation, assigning a value to each database attribute.

A set of database tuples with the same named database attributes; unlike an SQL result without duplicate elimination, a mathematical database relation has no repeated database tuples.