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Published online by Cambridge University Press:  12 March 2014

Jakob Kellner
Kurt Gödel Research Center For Mathematical Logic, Universität Wien, Währinger Strasse 25, 1090 Wien, Austria, E-mail:, URL:
Saharon Shelah
Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA, URL:


We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. As an application, we introduce a new method to force (weak) measurability of all definable sets with respect to a certain (non-ccc) ideal.

Research Article
Copyright © Association for Symbolic Logic 2011

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