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A new condensation principle

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Abstract.

We generalize ∇(A), which was introduced in [Sch∞], to larger cardinals. For a regular cardinal κ>ℵ0 we denote by ∇ κ (A) the statement that and for all regular θ>κ,

is stationary in

It was shown in [Sch∞] that can hold in a set-generic extension of L. We here prove that can hold in a set-generic extension of L as well. In both cases we in fact get equiconsistency theorems. This strengthens results of [Rä00] and [Rä01]. is equivalent with the existence of 0#.

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References

  1. Friedman, Sy: Fine structure and class forcing. Berlin, New York, deGruyter, 2000

  2. Jech, Thomas: Set theory. San Diego, 1978

  3. Räsch, Thoralf: Erweiterbarkeit von Einbettungen. Diplomarbeit, Humboldt-Universität zu Berlin, 2000

  4. Räsch, Thoralf: Extendibility of embeddings. Acta Univ. Carol. Math. Phys. 42 (2), 75–88 (2001)

    Google Scholar 

  5. Schindler, Ralf: Proper forcing and remarkable cardinals. Bull. Symb. Logic 6, 176–184 (2000)

    MATH  Google Scholar 

  6. Schindler, Ralf: Proper forcing and remarkable cardinals II. J. Symb. Logic. to appear

  7. Shelah, Saharon: Proper and improper forcing. Springer Verlag, 1998

  8. Shelah, Sarahon: E-mail (to Thoralf Räsch), dated June 21, 1999

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Authors and Affiliations

  1. Institut für Mathematik, Universität Potsdam, Postfach 60 15 53, 14415, Potsdam, Germany

    Thoralf Räsch

  2. Institut für mathematische Logik und Grundlagenforschung, Westfälische Wilhelms–Universität Münster, Einsteinstraße 62, 48149, Münster, Germany

    Ralf Schindler

Authors
  1. Thoralf Räsch
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  2. Ralf Schindler
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Correspondence to Ralf Schindler.

Additional information

Mathematics Subject Classification (1991): Primary 03E55, 03E15, Secondary 03E35, 03E60

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Räsch, T., Schindler, R. A new condensation principle. Arch. Math. Logic 44, 159–166 (2005). https://doi.org/10.1007/s00153-004-0227-1

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  • DOI: https://doi.org/10.1007/s00153-004-0227-1

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