Purity in model theory

This paper surveys the basic model-theoretic aspects of purity and presents ‘pure’ versions of some embedding, preservation, and Birkhoff type theorems, like the pure embeddability of direct limits in reduced products (Cor. 7.4) and a description of classes axiomatizable by implications of positive primitive formulas (a generalization of Mal’tsev’s quasi-varieties) in terms of reduced product, direct limit, and pure substructure (Thm.8.1).