Abstract
The aim of this short note is to correct an error in the proof in [1], more precisely in Remark 1 on page 395, where it is stated that any improper word has rank ≥2. This claim is false; and, consequently, Remark 2, asserting that any 1,0-deduction does not contain improper Q-terms, also fails immediately. In fact, let us consider the wordIt is easily seen that the rank of W is 1, but W is obviously improper. We remark that it is possible, in the same way, to give examples of improper words of rank 1 containing (without subordination) ε-subterms of arbitrarily high rank. In the following section we sketch a corrected version of the proof in order to eliminate all improper ε-terms.We refer to the notation and definitions of [1]. A more extended description of the theories involved can be found in [2].
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