Abstract.
We present several models which satisfy CH and some ♦-like principles while others fail, answering a question of Moore, Hrušák and Džamonja.
Similar content being viewed by others
References
Bagaria, J.: Fragments of Martin’s Axiom and Δ31 Sets of Reals. Ann. Pure Appl. Logic 691, 1–25 (1994)
Bartoszyński, T., Judah, H.: Set theory. A K Peters, Ltd., Wellesley, MA, 1995
Blass, A.: Reductions Between Cardinal Characteristics of the Continuum. Contemp. Math. 192, 31–49 (1996)
Brendle, J.: Cardinal invariants of the continuum and combinatorics on uncountable cardinals. Preprint
Brendle, J.: How to force it? lecture notes
Devlin, K.J.: Constructibility. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1984
Devlin, K.J., Shelah, S.: A weak version of ♦ which follows from Israel J. Math. 29 (2–3), 239–247 (1978).
Dow, A.: More set-theory for topologists. Topology Appl. 64 (3), 243–300 (1995)
Hrušák, M.: Another-♦-like principle, Fund. Math. 167 (3), 277–289 (2001)
Jensen, R.B.: Souslin’s hypothesis is incompatible with V=L(Abstract). Notices Am. Math. Soc. 15, 935 (1968)
Kunen, K.: Set Theory. Studies in Logic and the Foundations of Mathematics, 102. North-Holland Publishing Co., Amsterdam, 1983
Kunen, K.: Random and Cohen reals. Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 887–911
Moore, J.T., Hrušák, M., Džamonja, M.: Parametrized ♦ principles. Trans. Am. Math. Soc 356, 2281–2306 (2004)
Shelah, S.: Proper and Improper Forcing. Second edition. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1998
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
Truss, J.: Connections between different amoeba algebras. Fund. Math. 130 (2), 137–155 (1988)
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
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00153-004-0269-4