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Preserving preservation

Published online by Cambridge University Press:  12 March 2014

Jakob Kellner
Institut für Diskrete Mathematik und Geometrie, Technische Universitat Wien, 1050 Wien, AustriaE-mail:,, URL:
Saharon Shelah
Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israeland, Department of Mathematics, Rutgers University, New Brunswick, NJ 08854. USA, E-mail:,, URL:


We prove that the property “P doesn't make the old reals Lebesgue null” is preserved under countable support iterations of proper forcings, under the additional assumption that the forcings are nep (a generalization of Suslin proper) in an absolute way. We also give some results for general Suslin ccc ideals.

Research Article
Copyright © Association for Symbolic Logic 2005

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