Do All SQL Tables, Including Empty Ones, Possess Superkeys?

SQL Superkeys: A Comprehensive Explanation

A superkey in SQL is a set of columns that, if designated as a primary key or a unique NOT NULL constraint, would prevent duplicate rows and NULL values. This definition, however, requires nuanced consideration for empty and non-empty tables.

Empty Tables and Superkeys

An empty SQL table, devoid of any rows, possesses a unique property: every subset of its columns constitutes a superkey. This stems from the definition's focus on potential values; an empty table is considered capable of holding all possible values, thus satisfying the superkey condition for any column combination.

Non-Empty Tables and Superkeys

All non-empty SQL tables inherently contain at least one superkey. A table without duplicate rows and NULL values is essentially a relational model (RM) relation. RM relations, by definition, always possess one or more superkeys.

Bridging the Gap: SQL and the Relational Model

It's crucial to remember that SQL tables aren't perfectly aligned with the strict rules of RM relations. SQL allows for duplicates and NULLs, unlike RM relations. Consequently, the concept of a superkey in SQL is a practical extension, not a direct translation, of the RM concept.

A Practical Definition of SQL Superkeys

Considering the differences, we can define SQL superkeys as follows:

• Column sets that, when declared as primary keys or unique NOT NULL constraints, would eliminate duplicate rows and NULL values.
• In empty tables, all column subsets are superkeys.
• In non-empty tables without duplicates or NULLs, superkeys mirror those of their equivalent RM relation.

Key Terminology Clarification

• Candidate Keys (CKs): Minimal superkeys; they cannot be further reduced while maintaining their superkey properties.
• Primary Key: A chosen CK that uniquely identifies each row.
• Foreign Keys (FKs): Unlike superkeys, FKs define relationships between tables. They don't directly relate to the uniqueness or integrity of a single table.

In summary, while the concept of a superkey in SQL is adapted from the relational model, its application to empty tables reveals a unique characteristic, underscoring the important distinctions between SQL and the formal relational model.

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