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On descendingly complete ultrafilters

Set Theory And Combinatorics

Part of the Lecture Notes in Mathematics book series (LNM,volume 337)

Keywords

  • Regular Cardinal
  • Measurable Cardinal
  • Ultra Filter
  • Limit Cardinal
  • Inaccessible Cardinal

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Chang, C. C., Descendingly incomplete ultrafilters, Trans. Amer. Math. Soc. 126, 108–118 (1967).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. _____, Methods of constructing models, Sets, models and recursion theory, Edit. J. N. Crossley, Amsterdam 85–121 (1967).

    Google Scholar 

  3. Chudnovsky, G. V. and Chudnovsky, D. V., Regularnye i ubyvajusche nepolnye ultrafiltry, Dokl. Akad. Nauk SSSR 198, 779–782 (1971).

    MathSciNet  Google Scholar 

  4. Hajnal, A., Ulam-matrices for inaccessible cardinals, Bull. Acad. Polon. Sci. XVII, 683–688 (1969).

    MathSciNet  MATH  Google Scholar 

  5. Jorgensen, M. A., Images of ultrafilters and cardinality of ultrapowers, Amer. Math. Soc. Notices 18, 826 (1971).

    Google Scholar 

  6. _____, Regular ultrafilters and long ultrapowers, Ibid., 928.

    Google Scholar 

  7. Keisler, H. J., On cardinalities of ultraproducts, Bull. Amer. Math. Soc. 70, 644–647 (1964).

    CrossRef  MathSciNet  MATH  Google Scholar 

  8. Keisler, H. J. and Tarski, A., From accessible to inaccessible cardinals, Fund. Math. 53, 225–308 (1964).

    MathSciNet  MATH  Google Scholar 

  9. Ketonen, J., Everything you wanted to know about ultrafilters, Doctoral Dissertation, Univ. of Wisconsin, (1971).

    Google Scholar 

  10. Kunen, K. and Prikry, K., On descendingly incomplete ultrafilters, to appear in J. Symb. Logic.

    Google Scholar 

  11. Prikry, K., Changing measurable into accessible cardinals, Dissertationes Mathematicae (Rozprawy Matematyczne) LXVIII, 5–52 (1970).

    MathSciNet  MATH  Google Scholar 

  12. Prikry, K. and Shelah, S., On decomposability of families of sets, to appear.

    Google Scholar 

  13. Silver, J. H., Some applications of model theory in set theory, Ann. Math. Logic (1), 3, 45–110 (1971).

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Solovay, R., A Δ 13 non-constructible set of integers, Trans. Amer. Math. Soc. 127, 50–75 (1967).

    MathSciNet  MATH  Google Scholar 

  15. Ulam, S., Zur Masstheorie in der allgemeinen Mengelehre, Fund. Math. 16, 140–150 (1930).

    MATH  Google Scholar 

  16. Jensen, R. B., The fine structure of the constructible hierarchy, to appear in Annals of Math. Logic.

    Google Scholar 

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Dedicated to Professor A. Mostowski

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© 1973 Springer-Verlag

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Prikry, K. (1973). On descendingly complete ultrafilters. In: Mathias, A.R.D., Rogers, H. (eds) Cambridge Summer School in Mathematical Logic. Lecture Notes in Mathematics, vol 337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066785

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  • DOI: https://doi.org/10.1007/BFb0066785

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05569-3

  • Online ISBN: 978-3-540-36884-7

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