Advertisement

Set Theory pp 245-250 | Cite as

Postscript II: Infinitary Combinatorics

  • Abhijit Dasgupta
Chapter

Abstract

The topics of the last chapter (Chap. 11) naturally lead to the area of Infinitary Combinatorics, which is beyond the scope of this text. This postscript to Part II is intended to be a link for the reader to begin further study in the area. We indicate how the obvious generalizations of three separate topics of the last chapter, namely short orders, König’s Infinity Lemma, and Ramsey’s Theorem, converge naturally to the notion of a weakly compact cardinal, an example of a large cardinal. In addition, it is shown how Suslin’s Problem is equivalent to the existence of Suslin trees. Finally, we briefly mention Martin’s Axiom and Jensen’s Diamond principle \(\diamond \), and their implications for the Suslin Hypothesis.

References

  1. 14.
    F. R. Drake. Set theory: An Introduction to Large Cardinals. North Holland, 1974.Google Scholar
  2. 34.
    T. Jech. Set theory: The Third Millennium Edition. Springer, 2003.Google Scholar
  3. 35.
    W. Just and M. Weese. Discovering Modern Set Theory, I and II. American Mathematical Society, 1996, 1997.Google Scholar
  4. 37.
    A. Kanamori. The Higher Infinite. Springer, 2nd edition, 2003.Google Scholar
  5. 41.
    K. Kunen. Combinatorics. In Handbook of Mathematical Logic, pages 371–401. North Holland, 1977.Google Scholar
  6. 44.
    K. Kunen. Set Theory. College Publications, 2011.Google Scholar
  7. 48.
    A. Levy. Basic Set Theory. Dover, 2002.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Detroit MercyDetroitUSA

Personalised recommendations