Small $$\mathfrak {u}(\kappa )$$ u ( κ ) at singular $$\kappa $$ κ with compactness at $$\kappa ^{++}$$ κ + +

&
Archive for Mathematical Logic 61 (1):33-54 (2021)
  Copy   BIBTEX

Abstract

We show that the tree property, stationary reflection and the failure of approachability at \ are consistent with \= \kappa ^+ < 2^\kappa \), where \ is a singular strong limit cardinal with the countable or uncountable cofinality. As a by-product, we show that if \ is a regular cardinal, then stationary reflection at \ is indestructible under all \-cc forcings.

Categories

Add categories

Keywords

Reprint years

2022

DOI

10.1007/s00153-021-00776-5

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

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

Through your library

My notes

Similar books and articles

Strong Compactness and Stationary Sets.John Krueger - 2005 - Journal of Symbolic Logic 70 (3):767 - 777.
Undefinability of $kappa$-Well-Orderings in $L_{inftykappa}$.Juha Oikkonen - 1997 - Journal of Symbolic Logic 62 (3):999-1020.
Polarized Partition Relations.James Baumgartner & Andras Hajnal - 2001 - Journal of Symbolic Logic 66 (2):811-821.
On completeness of the quotient algebras {cal P}(kappa)/I.Yasuo Kanai - 2000 - Archive for Mathematical Logic 39 (2):75-87.
On skinny stationary subsets of.Yo Matsubara & Toschimichi Usuba - 2013 - Journal of Symbolic Logic 78 (2):667-680.
Borel reductions and cub games in generalised descriptive set theory.Vadim Kulikov - 2013 - Journal of Symbolic Logic 78 (2):439-458.
A characterization of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square(\kappa^{+})}$$\end{document} in extender models. [REVIEW]Kyriakos Kypriotakis & Martin Zeman - 2013 - Archive for Mathematical Logic 52 (1-2):67-90.
Small Forcing Makes any Cardinal Superdestructible.Joel Hamkins - 1998 - Journal of Symbolic Logic 63 (1):51-58.
On successors of Jónsson cardinals.J. Vickers & P. D. Welch - 2000 - Archive for Mathematical Logic 39 (6):465-473.
Indestructibility of the tree property.Radek Honzik & Šárka Stejskalová - 2020 - Journal of Symbolic Logic 85 (1):467-485.
Weak partition properties on trees.Michael Hrušák, Petr Simon & Ondřej Zindulka - 2013 - Archive for Mathematical Logic 52 (5-6):543-567.
Polarized partition relations.James E. Baumgartner & Andras Hajnal - 2001 - Journal of Symbolic Logic 66 (2):811-821.
On some small cardinals for Boolean algebras.Ralph Mckenzie & J. Donald Monk - 2004 - Journal of Symbolic Logic 69 (3):674-682.
$P_kappalambda$ Combinatorics II: The RK Ordering Beneath a Supercompact Measure.William S. Zwicker - 1986 - Journal of Symbolic Logic 51 (3):604-616.
Infinitary generalizations of deligne’s completeness theorem.Christian Espíndola - 2020 - Journal of Symbolic Logic 85 (3):1147-1162.

Analytics

Added to PP
2021-05-28

Downloads
16 (#886,588)

6 months
6 (#512,819)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

Aronszajn trees on ℵ2 and ℵ3.Uri Abraham - 1983 - Annals of Mathematical Logic 24 (3):213-230.
Reflecting stationary sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
Fragility and indestructibility of the tree property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.
Indestructibility of the tree property.Radek Honzik & Šárka Stejskalová - 2020 - Journal of Symbolic Logic 85 (1):467-485.
The eightfold way.James Cummings, Sy-David Friedman, Menachem Magidor, Assaf Rinot & Dima Sinapova - 2018 - Journal of Symbolic Logic 83 (1):349-371.

View all 14 references / Add more references