A note on Jónsson's theorem (Q1109763)

The author presents a model-theoretic proof of Jónsson's Theorem. Considering a type of algebras which have distributive lattices of congruences he proves that for any class of algebras \({\mathcal K}\) every subdirectly irreducible member \({\mathcal A}\) of the variety generated by \({\mathcal K}\) is a homomorphic image of a subalgebra of an ultraproduct of algebras in \({\mathcal K}\). The main step is to show that \({\mathcal A}\) is a model of the positive universal theory of \({\mathcal K}\).