Conflict Serializability and Two-Phase Locking
2PL produces exactly the serializable schedules; anomalies are precisely what you buy by weakening it.
Databases
Codd's Theorem
Relational algebra and relational calculus have equal expressive power. Why SQL is declarative and why a query planner can exist at all.
Paxos, Raft, and the Shape of Consensus
How real systems dodge FLP impossibility: safety always, liveness only when the network cooperates.
Quorum Intersection (R + W > N)
One inequality generating the entire read/write consistency tradeoff space.