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Chasing Silver

Published online by Cambridge University Press:  20 November 2018

Andrzej Rosłanowski
Affiliation:
Department of Mathematics, University of Nebraska at Omaha, Omaha, NE 68182-0243, U.S.A.. e-mail: roslanow@member.ams.org
Juris Steprāns
Affiliation:
Department of Mathematics, York University, Toronto, ON, M3J 1P3. e-mail: steprans@yorku.ca
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Abstract

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We show that limits of CS iterations of the $n$-Silver forcing notion have the $n$-localization property.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2008

References

[1] Cichoń, J., Rosłanowski, A., Steprāns, J., and Węglorz, B., Combinatorial properties of the ideal . J. Symbolic Logic 58(1993), no. 1, 4254.Google Scholar
[2] Dębski, W., Kleszcz, J., and Plewik, S., Perfect sets of independent functions. Acta Univ. Carolin. Math. Phys. 33(1992), no. 2, 3133.Google Scholar
[3] Geschke, S., More on convexity numbers of closed sets in n . Proc. Amer. Math. Soc. 133(2005), no. 5, 13071315 (electronic).Google Scholar
[4] Geschke, S. and Kojman, M., Convexity numbers of closed sets in n . Proc. Amer. Math. Soc. 130(2002), no. 10, 28712881 (electronic).Google Scholar
[5] Geschke, S., Kojman, M., Kubiś, W., and Schipperus, R., Convex decompositions in the plane and continuous pair colorings of the irrationals. Israel J. Math. 131(2002), 285317.Google Scholar
[6] Goldstern, M., Tools for your forcing construction. In: Set Theory of the Reals. Israel Math. Conf. Proc. 6, Bar-Ilan Univ., Ramat Gan, 1993, pp. 305360.Google Scholar
[7] Jech, T., Set theory. The third millennium edition, revised and expanded. Springer-Verlag, Berlin, 2003.Google Scholar
[8] Kamo, S., Some remarks about Mycielski ideals. Colloq. Math. 65(1993), no. 2, 291299.Google Scholar
[9] Kellner, J., Preserving non-null with Suslin+ forcing. Arch. Math. Logic 45(2006), no. 6, 649664.Google Scholar
[10] Mycielski, J., On the axiom of determinateness. I. Fund. Math. 59(1966), 203212.Google Scholar
[11] Mycielski, J., Some new ideals of sets on the real line. Coll. Math. 20(1969), 7176.Google Scholar
[12] Newelski, L. and Rosłanowski, A., The ideal determined by the unsymmetric game. Proc. Amer. Math. Soc. 117(1993), no. 3, 823831.Google Scholar
[13] Rosłanowski, A., On game ideals. Colloq. Math. 59(1990), no. 2, 159168.Google Scholar
[14] Rosłanowski, A., Mycielski ideals generated by uncountable systems. Colloq. Math. 66(1994), no. 2, 187200.Google Scholar
[15] Rosłanowski, A., n-localization property. J. Symbolic Logic 71(2006), no. 3, 881902 Google Scholar
[16] Sharp, J. D. and Thomas, S., Uniformization problems and the cofinality of the infinite symmetric group. Notre Dame J. Formal Logic 35(1994), no. 3, 328345.Google Scholar
[17] Shelah, S., Properness without elementaricity. J. Appl. Anal. 10(2004), no. 2, 169289.Google Scholar
[18] Shelah, S. and Steprāns, J., The covering numbers of Mycielski ideals are all equal. J. Symbolic Logic 66(2001), no. 2, 707718.Google Scholar