Erratum to: n-Fold implicative basic logic is Gödel logic

Abstract

1. The proof of Proposition 5 is wrong. Equation (10) can be utilized only if the power of an element x is n, not if it is n 1 as is done in the proof. Moreover, an n ? 1 element Lukasiewicz chain is an explicit example that Proposition 5 does not hold: {1} is an n-fold implicative filter in that algebra, however, the Lukasiewicz product is not idempotent. 2. Corollary 6, Theorem 8 and Theorem 9 are based on Proposition 5, therefore also they do not hold. Since Godel logic trivially satisfies axiom (12), we can only say that Godel logic is an example of n-fold implicative basic logic, however, n-fold implicative basic logic is not, in general, Godel logic, contrary to the claim in Theorem 9. 3. The inaccuracy of Proposition 5 also implies that the problem of the relation of n-fold implicative basic logic and n-fold positive implicative basic logic remains open, contrary to what is alleged in the Conclusion.