Inverse system characterizations of the (hereditarily) just infinite property in profinite groups

We give criteria on an inverse system of finite groups that ensure the limit is just infinite or hereditarily just infinite. More significantly, these criteria are ‘universal’ in that all (hereditarily) just infinite profinite groups arise as limits of the specified form. This is a corrected and revised version of the article: ‘Inverse system characterizations of the (hereditarily) just infinite property in profinite groups’, Bull. LMS vol 44, 3 (2012) 413–425.