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The Hanf number of $ L\sb{\omega \sb{1}\omega \sb{1}}$


Author: Jouko Väänänen
Journal: Proc. Amer. Math. Soc. 79 (1980), 294-297
MSC: Primary 03E35; Secondary 03C75
DOI: https://doi.org/10.1090/S0002-9939-1980-0565357-7
MathSciNet review: 565357
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Abstract: A model of set theory is constructed in which the Hanf number of $ {L_{{\omega _1}{\omega _1}}}$ is below the first weakly compact cardinal. This answers a question of J. Silver.


References [Enhancements On Off] (What's this?)

  • [1] M. Dickmann, Large infinitary languages, North-Holland, Amsterdam, 1975. MR 0539973 (58:27450)
  • [2] H. Friedman, One hundred and two problems in mathematical logic, J. Symbolic. Logic 40 (1975), 113-129. MR 0369018 (51:5254)
  • [3] T. Jech, Set theory, Academic Press, New York, 1978. MR 506523 (80a:03062)
  • [4] A. Kanamori and M. Magidor, The evolution of large cardinal axioms in set theory, Higher Set Theory, Lecture Notes in Math., vol. 669, Springer-Verlag, Berlin and New York, 1978, pp. 99-275. MR 520190 (80b:03083)
  • [5] K. Kunen, Some applications of iterated ultrapowers in set theory, Ann. Math. Logic 1 (1970), 179-227. MR 0277346 (43:3080)
  • [6] -, Saturated ideals, J. Symbolic. Logic 43(1) (1978), 65-76. MR 495118 (80a:03068)
  • [7] M. Magidor, How large is the first strongly compact cardinal? or: A study on identity crises, Ann. Math. Logic 10 (1976), 33-58. MR 0429566 (55:2578)
  • [8] T. Menas, Consistency results concerning supercompactness, Trans. Amer. Math. Soc. 223 (1976), 61-91. MR 0540771 (58:27488)
  • [9] J. Silver, Some applications of model theory in set theory, Ann. Math. Logic 3 (1971), 45-110. MR 0409188 (53:12950)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0565357-7
Article copyright: © Copyright 1980 American Mathematical Society

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