P-ideal dichotomy and weak squares

Journal of Symbolic Logic 78 (1):157-167 (2013)
  Copy   BIBTEX

Abstract

We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes ${\square}_{\kappa, \omega}$ for any uncountable $\kappa$. We also show that the P-ideal dichotomy implies the failure of ${\square}_{\kappa, < \mathfrak{b}}$ provided that $cf(\kappa) > {\omega}_{1}$

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,127

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Ideals Over $\omega$ and Cardinal Invariants of the Continuum.P. Matet & J. Pawlikowski - 1998 - Journal of Symbolic Logic 63 (3):1040-1054.
Weak partition properties on trees.Michael Hrušák, Petr Simon & Ondřej Zindulka - 2013 - Archive for Mathematical Logic 52 (5-6):543-567.
On skinny stationary subsets of.Yo Matsubara & Toschimichi Usuba - 2013 - Journal of Symbolic Logic 78 (2):667-680.
On completeness of the quotient algebras {cal P}(kappa)/I.Yasuo Kanai - 2000 - Archive for Mathematical Logic 39 (2):75-87.
Normality and $\mathscr{P}(\kappa)/\mathscr{J}$.R. Zrotowski - 1991 - Journal of Symbolic Logic 56 (3):1064-1067.
Weak square bracket relations for P κ (λ).Pierre Matet - 2008 - Journal of Symbolic Logic 73 (3):729-751.
Splitting number at uncountable cardinals.Jindřich Zapletal - 1997 - Journal of Symbolic Logic 62 (1):35-42.
Splitting Number at Uncountable Cardinals.Jindrich Zapletal - 1997 - Journal of Symbolic Logic 62 (1):35-42.
Normality and p(κ)/j.R. Zrotowski - 1991 - Journal of Symbolic Logic 56 (3):1064-1067.
Splitting $P_kappalambda$ into Stationary Subsets.Yo Matsubara - 1988 - Journal of Symbolic Logic 53 (2):385-389.

Analytics

Added to PP
2013-01-24

Downloads
86 (#201,793)

6 months
15 (#185,276)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

Set mapping reflection.Justin Tatch Moore - 2005 - Journal of Mathematical Logic 5 (1):87-97.
Combinatorial dichotomies in set theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.

Add more references