Hostname: page-component-6587cd75c8-rlsgg Total loading time: 0 Render date: 2025-04-24T02:07:15.755Z Has data issue: false hasContentIssue false
  • English
  • Français

Preserving preservation

Published online by Cambridge University Press:  12 March 2014

Jakob Kellner  and
Saharon Shelah
Jakob Kellner
Affiliation:
Institut für Diskrete Mathematik und Geometrie, Technische Universitat Wien, 1050 Wien, AustriaE-mail:, [email protected], URL: http://www.logic.univie.ac.at/~kellner
Saharon Shelah
Affiliation:
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:, [email protected], URL: http://www.math.rutgers.edu/~shelah
Get access Rights & Permissions [Opens in a new window]

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 ideals.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 3 , September 2005 , pp. 914 - 945
Copyright
Copyright © Association for Symbolic Logic 2005

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

[1]Bartoszynski, Tomek and Judah, Haim, Set theory: On the structure of the real line, A K Peters, Wellesley, MA, 1995.CrossRefGoogle Scholar
[2]Goldstern, Martin, Tools for Your Forcing Construction, Set theory of the reals (Judah, Haim, editor), Israel Mathematical Conference Proceedings, vol. 6, American Mathematical Society, 1993, pp. 305–360.Google Scholar
[3]Goldstern, Martin and Kellner, Jakob, New reals: Can live with them, can live without them, preprint, see http://arxiv.org/math.L0/0505471.Google Scholar
[4]Ihoda, Jaime (Judah, Haim) and Shelah, Saharon, Souslin forcing, this Journal, vol. 53 (1988), pp. 1188–1207.Google Scholar
[5]Jech, Thomas, Set theory, Monographs in mathematics, Springer-Verlag, 2002, 3rd millennium ed.Google Scholar
[6]Kanamori, Akihiro, The higher infinite, Perspectives in Mathematical Logic, Springer-Verlag, 1994.Google Scholar
[7]Kellner, Jakob, Preserving non-null with Suslin+ forcings, preprint, see http://arxiv.org/math.LO/0211385.Google Scholar
[8]Repicky, Miroslav, Goldstern-Judah-Shelah preservation theorem for countable support iterations, Fundamenta Mathematicae, vol. 144 (1994), pp. 55–72.CrossRefGoogle Scholar
[9]Roslanowski, Andrzej and Shelah, Saharon, Measured creatures, Israel Journal of Mathematics, accepted, math.LO/0010070.Google Scholar
[10]Schlindwein, Chaz, A short proof of the preservation of the ωω-bounding property, Mathematical Logic Quarterly, vol. 50 (2004), no. 1, pp. 29–32.CrossRefGoogle Scholar
[11]Schlindwein, Chaz, Understanding preservation theorems: omega-omega bounding, preprint, see http://arxiv.org/math.LO/0505645.Google Scholar
[12]Shelah, Saharon, Proper and improper forcing, Perspectives in Mathematical Logic, Springer-Verlag, 1998.CrossRefGoogle Scholar
[13]Shelah, Saharon, Properness without elementaricity, Journal of Applied Analysis, vol. 10 (2004), pp. 168–289, math.L0/9712283.CrossRefGoogle Scholar
[14]Solovay, R. M. and Tennenbaum, S., Iterated Cohen extensions and Souslin's problem, Annals of Mathematics. Second Series, vol. 94 (1971), pp. 201–245.CrossRefGoogle Scholar
[15]Zapletal, Jindřich, Descriptive set theory and definable forcing, Memoirs of the American Mathematical Society, vol. 167, 3 (2004), no. 793.CrossRefGoogle Scholar