We study a convergence phenomenon in the projective limit model A°° for PA, an axiom\ud system in the framework of process algebra for processes built from atomic actions by\ud means of alternative. composition (+) and sequential composition and subject to the\ud operations 11 (merge) and IL (left-merge). The model A°° is also a complete metric space.\ud Specifically, it is shown that for every element q E A°° the sequence q, s(q), s2(q), ... ,\ud sn(q), ... converges to a solution of the (possibly unguarded) recursion equation X = s(X)\ud where s(X) is an expression in the signature of PA involving the recursion variable X. As\ud the convergence holds for arbitrary starting points q, this result does not seem readily\ud obtainable by the usual convergence proof techniques. Furthermore, the connection is\ud studied between projective models and models based on process graphs. Also these models\ud are compared with the process model introduced by De Bakker and Zucker
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