Abstract
This paper introduces the concepts of R 0 valuation, R 0 semantic, countable R 0 category $$\mathcal{C}R_0$$ , R 0 fuzzy topological category $$\mathcal{R}CG$$ , etc. It is established in a natural way that the fuzzy topology ? and its cut topology on the set Ω M consisting of all R 0 valuations of an R 0 algebra M, and some properties of fuzzy topology ? and its cut topology are investigated carefully. Moreover, the representation theorem for R 0 algebras by means of fuzzy topology is given, that is to say the category $$\mathcal{C}R_0$$ is equivalent to the category $$\mathcal{R}CG^{op}$$ . By studying the relation between valuations and filters, the Loomis---Sikorski theorem for R 0 algebras is obtained. As an application, K-compactness of the R 0 logic $$\mathcal{L}^{*}$$ is discussed.
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