El teorema de Birkhoff

Abstract

[en] Birkhoff’s Theorem states that let K be a class of algebras, then K is an equational class if, only if, K is a variety. To reach this result, is necessary to understand some basic concepts of universal algebra. Varieties, free algebras and identities will be essential to understand the proof of Birkhoff’s Theorem. We study that statement and how to achieve the proof of it. We also study some of the immediate consequeces of Birkhoff’s Theorem in equational logic. Moreover, there is a final section as appendix where we study some properties of lattices.