Israel Journal of Mathematics

, Volume 49, Issue 4, pp 315–324 | Cite as

On Jónsson cardinals with uncountable cofinality

  • Jan Tryba


For a regular cardinal κ a Jónsson model of size κ+ is presented. We notice that every singular Jónsson cardinal κ with uncountable cofinality is the limit of some continuous sequence of smaller Jónsson cardinals. An analogous statement holds if κ is an inaccessible Jónsson cardinal unless κ is Mahlo. But we prove that the first Mahlo cardinal cannot be Jónsson. Some additional remarks are included.


Regular Cardinal Measurable Cardinal Elementary Embedding Generic Filter 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    K. J. Devlin,Some remarks on changing cofinalities, J. Symb. Logic39 (1974), 27–30.CrossRefMathSciNetMATHGoogle Scholar
  2. 2.
    D. Donder, R. B. Jensen and B. J. Koppelberg,Some applications of the core model, inSet Theory and Model Theory (R. B. Jensen and A. Prestel, eds.), Springer Lecture Notes in Mathematics872, 1981, pp. 55–97.Google Scholar
  3. 3.
    P. Erdös and A. Hajnal,On a problem of B. Jónsson, Bull. Acad. Pol. Sci., Ser. Sci. Math., Astron. Phys.14 (1966), 19–23.MATHGoogle Scholar
  4. 4.
    A. Kanamori,Weakly normal filters and irregular ultrafilters, Trans. Am. Math. Soc.220 (1976), 393–399.CrossRefMathSciNetMATHGoogle Scholar
  5. 5.
    A. Kanamori and M. Magidor,The evolution of large cardinal axioms in set theory, inHigher Set Theory (G. Müller and D. Scott, eds.), Springer Lecture Notes in Mathematics669, 1978, pp. 99–275.Google Scholar
  6. 6.
    E. M. Kleinberg,The equiconsistency of two large cardinal axioms, Fundam. Math.102 (1979), 81–85.MathSciNetGoogle Scholar
  7. 7.
    K. Kunen,Some applications of iterated ultrapowers in set theory, Ann. Math. Log.1 (1970), 179–227.CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    K. Prikry,Changing measurable into accessible cardinals, Diss. Math.68 (1970), 5–52.MathSciNetGoogle Scholar

Copyright information

© Hebrew University 1984

Authors and Affiliations

  • Jan Tryba
    • 1
  1. 1.Department of MathematicsGdansk UniversityGdańskPoland

Personalised recommendations