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Our article [4] contained a number of algorithmic and structural results about finitely generated subgroups of residually free groups. While all the arguments and proofs given in [4] are internally consistent, our results in the most general form relied on Proposition 5.1 of [4], which we attributed to the paper [8] (that is currently in preparation and has an additional author, V. Remeslennikov). Unfortunately, it turns out that Proposition 5.1 is incorrect as stated by us in [4], as was pointed out to the author by Zlil Sela, Mladen Bestvina, Olga Kharlampovich, Alexei Myasnikov and Inna Bumagina after [4] appeared. This mistake was due to a failure of communication and misunderstanding on my part of the results of [8], and I take full responsibility for this event. All the main results of [4], namely Theorems A, B, C, and D, are thus incomplete and should be regarded as conjectures for the moment. It is clear to the author that these statements are in fact correct, but the proofs would require a careful and quite lengthy inductive use of Proposition 5.4 of [4] (that is due to A. Myasnikov and V. Remeslennikov [9]) together with the results of R. Burns [1], [2] and D. Cohen [3], instead of relying on the incorrect Proposition 5.1 as a shortcut. Nevertheless, all of the proofs given in [4] are correct and complete for the case of word-hyperbolic fully residually free groups, since in that case Proposition 5.1 was not needed. Thus what was actually proved in [4] can be summarized in the following:

Erratum to “Subgroup properties of fully residually free groups”