Skip to main content
Log in

Diamond principles in Cichoń’s diagram

  • Published:
Archive for Mathematical Logic Aims and scope Submit manuscript

Abstract.

We present several models which satisfy CH and some ♦-like principles while others fail, answering a question of Moore, Hrušák and Džamonja.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bagaria, J.: Fragments of Martin’s Axiom and Δ31 Sets of Reals. Ann. Pure Appl. Logic 691, 1–25 (1994)

    Article  Google Scholar 

  2. Bartoszyński, T., Judah, H.: Set theory. A K Peters, Ltd., Wellesley, MA, 1995

  3. Blass, A.: Reductions Between Cardinal Characteristics of the Continuum. Contemp. Math. 192, 31–49 (1996)

    Google Scholar 

  4. Brendle, J.: Cardinal invariants of the continuum and combinatorics on uncountable cardinals. Preprint

  5. Brendle, J.: How to force it? lecture notes

  6. Devlin, K.J.: Constructibility. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1984

  7. Devlin, K.J., Shelah, S.: A weak version of ♦ which follows from Israel J. Math. 29 (2–3), 239–247 (1978).

    Google Scholar 

  8. Dow, A.: More set-theory for topologists. Topology Appl. 64 (3), 243–300 (1995)

    Article  Google Scholar 

  9. Hrušák, M.: Another-♦-like principle, Fund. Math. 167 (3), 277–289 (2001)

    Google Scholar 

  10. Jensen, R.B.: Souslin’s hypothesis is incompatible with V=L(Abstract). Notices Am. Math. Soc. 15, 935 (1968)

    Google Scholar 

  11. Kunen, K.: Set Theory. Studies in Logic and the Foundations of Mathematics, 102. North-Holland Publishing Co., Amsterdam, 1983

  12. Kunen, K.: Random and Cohen reals. Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 887–911

  13. Moore, J.T., Hrušák, M., Džamonja, M.: Parametrized ♦ principles. Trans. Am. Math. Soc 356, 2281–2306 (2004)

    Article  Google Scholar 

  14. Shelah, S.: Proper and Improper Forcing. Second edition. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1998

  15. Truss, J.: Sets having calibre ℵ1. Logic Colloquium 76 (Oxford, 1976), Studies in Logic and Found. Math., Vol. 87, North-Holland, Amsterdam, 1977, pp. 595–612

  16. Truss, J.: Connections between different amoeba algebras. Fund. Math. 130 (2), 137–155 (1988)

    Google Scholar 

  17. Vojtaš, P.: Generalized Galois-Tukey-connections between explicit relations on classical objects of real analysis. Set theory of the reals (Ramat Gan, 1991), Israel Math. Conf. Proc., 6, Bar-Ilan Univ., Ramat Gan, 1993, pp. 619–643

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hiroaki Minami.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Minami, H. Diamond principles in Cichoń’s diagram. Arch. Math. Logic 44, 513–526 (2005). https://doi.org/10.1007/s00153-004-0269-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00153-004-0269-4

Keywords

Navigation