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Keywords:

  • n -localization property;
  • weak Sacks property;
  • countable support iterations;
  • ergodic iteration theorem

Abstract

I prove several natural preservation theorems for the countable support iteration. This solves a question of Rosłanowski regarding the preservation of localization properties and greatly simplifies the proofs in the area (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)