Databases · Cluster
Relational Model
Relations, normalization, and integrity.
- 01 Relations as Sets: Why the Relational Model Excludes Duplicate Rows How Codd defined a relation as a subset of a Cartesian product, what follows from value-based identity, and why SQL tables are multisets instead.
- 02 Attribute Closure and the Mechanical Derivation of Candidate Keys How Armstrong axioms generate the closure of a dependency set, why closure of an attribute set is computed by repeated scanning, and how to enumerate minimal keys without exponential search.
- 03 Referential Integrity and the Semantics of Foreign Key Actions What a foreign key actually asserts, how each ON DELETE and ON UPDATE action resolves the violated constraint, and why MATCH SIMPLE accepts a partially null key.
- 04 Boyce-Codd Normal Form and the Cost of Losing a Dependency Why BCNF decomposition can make a functional dependency unverifiable without a join, how 3NF avoids that, and when the extra anomaly is the better trade.
- 05 Multivalued Dependencies and the Redundancy BCNF Cannot See How an MVD asserts independence between two attribute groups, why the four-way combination of independent lists forces redundancy, and how 4NF decomposes on it.
- 06 Nulls, Three-Valued Logic, and the Constraints They Break How UNKNOWN propagates through SQL predicates, why NOT IN behaves unexpectedly with nulls, and which integrity constraints a null silently satisfies.
- 07 The Chase as a General Test for Dependency Implication How the chase algorithm decides whether a decomposition is lossless and whether one dependency set implies another, and why its termination is guaranteed but its runtime is not.
- 08 Join Dependencies and the Ternary Structure Fifth Normal Form Protects Why a relation can be pairwise lossless and still not be a join of two projections, how a three-way join dependency arises from a cyclic constraint, and what 5NF removes.
- 09 Inclusion Dependencies and the Undecidability That Follows Them How inclusion dependencies generalize foreign keys across arbitrary attribute sets, why their implication problem needs infinite chase sequences, and what breaks when they are combined with functional dependencies.
- 10 Sixth Normal Form and the Cost of One Attribute per Relation How a decomposition into key-plus-one-attribute relations removes every update anomaly by construction, what the extra joins cost, and which workloads make that cost worth paying.