Good sequences without subdirect representation: a constructive treatment of Mundici’s $${{\,\mathrm{\mathbf {\Gamma }}\,}}$$ functor

Abstract Good sequences are central to Mundici’s categorical equivalence between MV-algebras and unital $$\ell $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> -groups. We eliminate the reliance on Chang’s subdirect representation theorem traditionally used in the proof, replacing it with an entirely constructive argument based on entailment relations.