Iterated rings of bounded elements: Erratum
  We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of Schm\"udgen's Positivstellensatz" [2].   [1] Universit\"at Konstanz (2001), available at http://www.ub.uni-konstanz.de/kops/volltexte/2002/825/   [2] Journal f\"ur die reine und angewandte Mathematik 554, 19-45 (2003) 
Markus Schweighofer