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Preserving preservation

  • Jakob Kellner (a1) and Saharon Shelah (a2)

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.

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[10] Chaz Schlindwein , A short proof of the preservation of the ωω-bounding property, Mathematical Logic Quarterly, vol. 50 (2004), no. 1, pp. 2932.

[12] Saharon Shelah , Proper and improper forcing, Perspectives in Mathematical Logic, Springer-Verlag, 1998.

[13] Saharon Shelah , Properness without elementaricity, Journal of Applied Analysis, vol. 10 (2004), pp. 168289, math.L0/9712283.

[14] R. M. Solovay and S. Tennenbaum , Iterated Cohen extensions and Souslin's problem, Annals of Mathematics. Second Series, vol. 94 (1971), pp. 201245.

[15] Jindřich Zapletal , Descriptive set theory and definable forcing, Memoirs of the American Mathematical Society, vol. 167, 3 (2004), no. 793.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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