1. (Note that the references have no claim (or either completeness nor historic accuracy concerning priorities. They merely reflect the authors accidental readings.)
2. Generalisation of variety and quasivariety concepts to partial algebras through category theory;Andreka;Dissertationes Mathematicae (Rozprawy Math.),1983
3. Subcategories defined by implications;Banasehewski;Houston Journal of Mathematics,1976
4. Higher Model Theory: Logic of Mathematical Concepts;Barwise,1983