Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-16T23:07:54.339Z Has data issue: false hasContentIssue false
  • English
  • Français

Suslin forcing and parametrized ◊ principles

Published online by Cambridge University Press:  12 March 2014

Hiroaki Minami
Hiroaki Minami*
Affiliation:
Graduate School of Science and Technology, Kobe University, Rokkodai, Nada-Ku, Kobe 657-8501, Japan, E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

By using finite support iteration of Suslin c.c.c forcing notions we construct several models which satisfy some ◊-like principles while other cardinal invariants are larger than ω1.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 752 - 764
Copyright
Copyright © Association for Symbolic Logic 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bartoszyński, Tomek and Judah, Haim, Set theory. On the structure of the real line, A K Peters, Wellesley, MA, 1995.Google Scholar
[2]Blass, Andreas, Reductions between cardinal characteristics of the continuum, Contemporary Mathematics, vol. 192 (1996), pp. 31–49.CrossRefGoogle Scholar
[3]Blass, Andreas, Combinatorial cardinal characteristics of the continuum, Handbook of set theory (Foreman, Matthew and Kanamori, Akihiro, editors), Springer-Verlag, Berlin, to appear.Google Scholar
[4]Kunen, Kenneth, Set theory. An introduction to independence proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co, Amsterdam, 1983.Google Scholar
[5]Miller, Arnold W., Some properties of measure and category, Transactions of the American Mathematical Society, vol. 266 (1981), no. 1, pp. 93–114.CrossRefGoogle Scholar
[6]Minami, Hiroaki, Diamond principles in Cichoń's diagram, Archive for Mathematical Logic, (2005), no. 4, pp. 513–526.Google Scholar
[7]Moore, Justin Tatch, Hrušák, Michael, and Džamonja, Mirna, Parametrized ◊ principles, Transactions of the American Mathematical Society, vol. 356 (2004), pp. 2281–2306.CrossRefGoogle Scholar