[_hardwaregeek]

Likewise this is a pretty useful chain of inclusions:

commutative rings ⊃ integral domains ⊃ integrally closed domains ⊃ GCD domains ⊃ unique factorization domains ⊃ principal ideal domains ⊃ Euclidean domains ⊃ fields ⊃ finite fields

[vortico]

Was just about to post that. You can get very fine-grained from sets to any mathematical structure based on sets, where the inclusion chain is a spectrum of structureless to structured.