Relational schema

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.