Abstract We uncover a connection between the model-theoretic notion of superstability and that noetherian rings pure-semisimple rings. characterize via class left modules with embeddings. Theorem 0.1 For ring R following are equivalent. (1) is noetherian. (2) The R-modules embeddings superstable. (3) every ? ? | + ? 0 , there ? such has uniqueness limit models cardinality ?. (4) Every model in ...

Injective Pure Type Systems form a large class of Pure Type Systems for which one can compute by purely syntactic means two sorts elmt(?jM) and sort(?jM), where ? is a pseudo-context and M is a pseudo-term, and such that for every sort s, ? ` M : A ^ ? ` A : s) elmt(?jM) = s ? ` M : s) sort(?jM) = s By eliminating the problematic clause in the (abstraction) rule in favour of constraints over el...