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Saccharinity

Published online by Cambridge University Press:  12 March 2014

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, Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08854, USA, URL: http://shelah.logic.at/
Corresponding
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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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2011

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References

[1]Brendle, Jörg, Mad families and iteration theory, Logic and algebra, Contemporary Mathematics, vol. 302, American Mathematical Society, Providence, RI, 2002, pp. 131.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. 135149.CrossRefGoogle Scholar
[3]Goldstern, Martin, A taste of proper forcing, Set theory (Curaçao, 1995; Barcelona, 1996), Kluwer Academic Publishers, Dordrecht, 1998, pp. 7182.Google Scholar
[4[Groszek, M. and Jech, T., Generalized iteration of forcing, Transactions of the American Mathematical Society, vol. 324 (1991), no. 1, pp. 126.CrossRefGoogle Scholar
[5]Groszek, Marcia, ω1* as an initial segment of the c-degrees, this Journal, vol. 59 (1994), no. 3, pp. 956976.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. 748755.CrossRefGoogle Scholar
[7]Kanovei, Vladimir, On non-wellfounded iterations of the perfect set forcing, this Journal, vol. 64 (1999), no. 2, pp. 551574.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. 583663.CrossRefGoogle Scholar
[11]Shelah, Saharon, Can you take Solovay's inaccessible away?, Israel Journal of Mathematics, vol. 48 (1984), no. 1, pp. 147.CrossRefGoogle Scholar
[12]Shelah, Saharon, Properness without elementaricity, Journal of Applied Analysis, vol. 10 (2004), no. 2, pp. 169289.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. 187223.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. 156.CrossRefGoogle Scholar
[15]Zapletal, Jindřich, Forcing idealized, Cambridge Tracts in Mathematics, vol. 174, Cambridge University Press, Cambridge, 2008.CrossRefGoogle Scholar

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