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Preserving Preservation
Journal of Symbolic Logic 70 (3):914 - 945 (2005)
Abstract
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 idealsOther Versions
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Citations of this work
New reals: Can live with them, can live without them.Martin Goldstern & Jakob Kellner - 2006 - Mathematical Logic Quarterly 52 (2):115-124.
Understanding preservation theorems, II.Chaz Schlindwein - 2010 - Mathematical Logic Quarterly 56 (5):549-560.
Understanding preservation theorems: chapter VI of Proper and Improper Forcing, I.Chaz Schlindwein - 2014 - Archive for Mathematical Logic 53 (1-2):171-202.
Many countable support iterations of proper forcings preserve Souslin trees.Heike Mildenberger & Saharon Shelah - 2014 - Annals of Pure and Applied Logic 165 (2):573-608.
References found in this work
Set Theory: On the Structure of the Real Line.T. Bartoszyński & H. Judah - 1999 - Studia Logica 62 (3):444-445.
A short proof of the preservation of the ωω‐bounding property.Chaz Schlindwein - 2004 - Mathematical Logic Quarterly 50 (1):29-32.
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