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Order Convergence and Distance on Lukasiewicz-Moisil Algebras
George Geordesce, Ionna Leustean and Andrei Popescu

The paper develops a study of order convergence in Lukasiewicz-Moisil algebras. An axiomatical notion of distance (covering the pointwise and the Heyting distances) is provided, together with an associated notion of Cauchy sequence. Under natural hypotheses, it is proven the existence of Cauchy completions. It is analyzed the connection to Boolean algebras along the canonical adjunction. The special class of proper LMm-algebras with Lukasiewicz distance is also investigated. Finally, we provide characterizations for the Cauchy completions corresponding to some particular class of axiomatic distances.

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