Axiomatizations of universal classes through infinitary logic
Michał M. Stronkowski · Algebra Universalis · 2018
We present a scheme for providing axiomatizations of universal classes. We use infinitary sentences there. New proofs of Birkhoff’s $$\mathsf {HSP}$$ -theorem and Mal’cev’s $$\mathsf {SPP_U}$$ -theorem are derived. In total, we present 75 facts of this sort.