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Preserving Non-null with Suslin+ Forcings

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Abstract

We introduce the notion of effective Axiom A and use it to show that some popular tree forcings are Suslin+. We introduce transitive nep and present a simplified version of Shelah’s “preserving a little implies preserving much”: If I is a Suslin ccc ideal (e.g. Lebesgue-null or meager) and P is a transitive nep forcing (e.g. P is Suslin+) and P does not make any I-positive Borel set small, then P does not make any I-positive set small.

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References

  1. Bagaria J., Bosch R. (1997) Projective forcing. Ann. Pure Appl. Logic 86(3): 237–266

    Article  MATH  MathSciNet  Google Scholar 

  2. Bartoszyński T., Judah H. Set theory: on the structure of the real line. In: Peters A.K., (ed) Wellesley (1995)

  3. Baumgartner J.E. (1983) Iterated forcing. In: Mathias A. (ed) Surveys in set theory, London mathematical society lecture note series, vol 87. Cambridge University Press, Cambridge, pp. 1–59

    Google Scholar 

  4. Goldstern M. Tools for your forcing construction. In: Judah H. (ed) Set Theory of The Reals, israel mathematical conference proceedings, vol. 6, pp. 305–360. American Mathematical Society (1993)

  5. Goldstern M., Judah H. (1992) Iteration of Souslin forcing, projective measurability and the Borel conjecture. Isr. J. Math. 78, 335–362

    Article  MATH  MathSciNet  Google Scholar 

  6. Ihoda (Haim Judah), J., Shelah S. Souslin forcing. J. Symb. Logic 53, 1188–1207 (1988)

    Google Scholar 

  7. Judah H., Shelah S. (1990) The kunen-miller chart (lebesgue measure, the baire property, laver reals and preservation theorems for forcing). J. Symb. Logic 55, 909–927

    Article  MATH  MathSciNet  Google Scholar 

  8. Keisler H.J. (1970) Logic with the quantifier “there exist uncountably many”. Ann. Math. Logic 1, 1–93

    Article  MATH  MathSciNet  Google Scholar 

  9. Kellner J., Shelah S. Preserving preservation. J. Symb. Logic 70(3), 914–945 (2005). Math. LO/0405081

  10. Pawlikowski J. Laver’s forcing and outer measure. In: Bartoszyński T., Scheepers M. (eds.) Proceedings of BEST conferences 1991–1994. American Mathematical Society, Providence (1995)

  11. Roslanowski A., Shelah S. Norms on possibilities i: forcing with trees and creatures. Memoirs of the American Mathematical Society, vol. 141, xii + 167 (1999). Math.LO/9807172

  12. Shelah S. (1998) Proper and improper forcing Perspectives in Mathematical Logic. Springer, Berlin Heidelberg New York

    Google Scholar 

  13. Shelah S. Properness without elementaricity. J. Appl. Anal. 10, 168–289 (2004). Math. LO/9712283

    Google Scholar 

  14. Sikorski R. (1964) Boolean Algebras. Springer, Berlin Heidelberg New York

    MATH  Google Scholar 

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  1. Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Straße 25, 1090, Wien, Austria

    Jakob Kellner

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  1. Jakob Kellner
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Correspondence to Jakob Kellner.

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Kellner, J. Preserving Non-null with Suslin+ Forcings. Arch. Math. Logic 45, 649–664 (2006). https://doi.org/10.1007/s00153-006-0008-0

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  • DOI: https://doi.org/10.1007/s00153-006-0008-0

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