Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T19:59:10.806Z Has data issue: false hasContentIssue false
  • English
  • Français

Saccharinity

Published online by Cambridge University Press:  12 March 2014

Jakob Kellner and
Saharon Shelah
Jakob Kellner
Affiliation:
Kurt Gödel Research Center For Mathematical Logic, Universität Wien, Währinger Strasse 25, 1090 Wien, Austria, E-mail: kellner@fsmat.at, 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, IsraelDepartment of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA, URL: http://shelah.logic.at/
Get accessRights & Permissions [Opens in a new window]

Abstract

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.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011, pp. 1153 - 1183
Copyright
Copyright © Association for Symbolic Logic 2011

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]Brendle, Jörg, Mad families and iteration theory, Logic and algebra, Contemporary Mathematics, vol. 302, American Mathematical Society, Providence, RI, 2002, pp. 1–31.CrossRefGoogle Scholar
[2]Brendle, Jörg, Halbeisen, Lorenz, and Löwe, Benedikt, Silver measurability and its relation to other regularity properties. Mathematical Proceedings of the Cambridge Philosophical Society, vol. 138 (2005), no. 1, pp. 135–149.CrossRefGoogle Scholar
[3]Goldstern, Martin, A taste of proper forcing, Set theory (Curaçao, 1995; Barcelona, 1996), Kluwer Academic Publishers, Dordrecht, 1998, pp. 71–82.Google Scholar
[4[Groszek, M. and Jech, T., Generalized iteration of forcing, Transactions of the American Mathematical Society, vol. 324 (1991), no. 1, pp. 1–26.CrossRefGoogle Scholar
[5]Groszek, Marcia, ω1* as an initial segment of the c-degrees, this Journal, vol. 59 (1994), no. 3, pp. 956–976.Google Scholar
[6]Jech, Thomas and Shelah, Saharon, A complete Boolean algebra that has no proper atomless complete subalgebra. Journal of Algebra, vol, 182 (1996), no. 3, pp. 748–755.CrossRefGoogle Scholar
[7]Kanovei, Vladimir, On non-wellfounded iterations of the perfect set forcing, this Journal, vol. 64 (1999), no. 2, pp. 551–574.Google Scholar
[8]Kellner, J., Non elementary proper forcing, preprint, http://arxiv.org/abs/0910.2132.Google Scholar
[9]Rosłanowski, Andrzej and Shelah, Saharon, Norms on possibilities. I. Forcing with trees and creatures. Memoirs of the American Mathematical Society, vol. 141 (1999), no. 671, pp. xii + 167.CrossRefGoogle Scholar
[10]Rosłanowski, Andrzej and Shelah, Saharon, Sweet & sour and other flavours of ccc forcing notions, Archive for Mathematical Logic, vol. 43 (2004), no. 5, pp. 583–663.CrossRefGoogle Scholar
[11]Shelah, Saharon, Can you take Solovay's inaccessible away?, Israel Journal of Mathematics, vol. 48 (1984), no. 1, pp. 1–47.CrossRefGoogle Scholar
[12]Shelah, Saharon, Properness without elementaricity, Journal of Applied Analysis, vol. 10 (2004), no. 2, pp. 169–289.CrossRefGoogle Scholar
[13]Shelah, Saharon, Two cardinal invariants of the continuum (∂a < α) and FS linearly ordered iterated forcing, Acta Mathematica, vol. 192 (2004), no. 2, pp. 187–223.CrossRefGoogle Scholar
[14]Solovay, Robert M., A model of set-theory in which every set of reals is Lebesgue measurable, Annals of Mathematics. Second Series, vol. 92 (1970), pp. 1–56.CrossRefGoogle Scholar
[15]Zapletal, Jindřich, Forcing idealized, Cambridge Tracts in Mathematics, vol. 174, Cambridge University Press, Cambridge, 2008.CrossRefGoogle Scholar