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In this paper, the author examines the notion of n-fold fantastic and fuzzy n-fold fantastic filters in BL-algebras. Several characterizations of fuzzy n-fold fantastic filters are given. The author shows that every n-fold (fuzzy n-fold) fantastic filter is a filter (fuzzy filter), but the converse is not true. Using a level set of a fuzzy set in a BL-algebra, the author gives a characterization of fuzzy n-fold fantastic filters. Finally, the author establishes the extension property for n-fold and fuzzy n-fold fantastic filters in BL-algebras. The author also constructs some algorithms for folding theory applied to fantastic filters in BL-algebras.

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We prove that Haveshki's and Eslami's n-fold implicative basic logic is Gödel logic and n-fold positive implicative basic logic is a fragment of ukasiewicz logic.