Stationary and closed rainbow subsets

&
Annals of Pure and Applied Logic 172 (2):102887 (2021)
  Copy   BIBTEX

Abstract

We study the structural rainbow Ramsey theory at uncountable cardinals. Compared to the usual rainbow Ramsey theory, the variation focuses on finding a rainbow subset that not only is of a certain cardinality but also satisfies certain structural constraints, such as being stationary or closed in its supremum. In the process of dealing with cardinals greater than ω1, we uncover some connections between versions of Chang's Conjectures and instances of rainbow Ramsey partition relations, addressing a question raised in [18].

Categories

Keywords

Reprint years

DOI

10.1016/j.apal.2020.102887

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,672

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

Destructibility of stationary subsets of Pκλ.Sakaé Fuchino & Greg Piper - 2005 - Mathematical Logic Quarterly 51 (6):560-569.
Indestructibility and stationary reflection.Arthur W. Apter - 2009 - Mathematical Logic Quarterly 55 (3):228-236.
On the existence of large subsets of [λ] κ which contain no unbounded non-stationary subsets.Saharon Shelah - 2002 - Archive for Mathematical Logic 41 (3):207-213.
Reflecting stationary sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
Forcing closed unbounded sets.Uri Abraham & Saharon Shelah - 1983 - Journal of Symbolic Logic 48 (3):643-657.
Splitting stationary sets in.Toshimichi Usuba - 2012 - Journal of Symbolic Logic 77 (1):49-62.
Forcing closed unbounded subsets of ω2.M. C. Stanley - 2001 - Annals of Pure and Applied Logic 110 (1-3):23-87.
On κ-like structures which embed stationary and closed unbounded subsets.James H. Schmerl - 1976 - Annals of Mathematical Logic 10 (3-4):289-314.
On -like structures which embed stationary and closed unbounded subsets.James H. Schmerl - 1976 - Annals of Mathematical Logic 10 (3):289.
Possible behaviours of the reflection ordering of stationary sets.Jiří Witzany - 1995 - Journal of Symbolic Logic 60 (2):534-547.
Splitting P κλ into stationary subsets.Yo Matsubara - 1988 - Journal of Symbolic Logic 53 (2):385-389.
Menas' conjecture and generic ultrapowers.Yo Matsubara - 1987 - Annals of Pure and Applied Logic 36:225-234.
Strong analogues of Martin's axiom imply axiom R.Robert E. Beaudoin - 1987 - Journal of Symbolic Logic 52 (1):216-218.
Local saturation of the non-stationary ideal over Pκλ.Toshimichi Usuba - 2007 - Annals of Pure and Applied Logic 149 (1-3):100-123.
Adding Closed Unbounded Subsets of ω₂ with Finite Forcing.William J. Mitchell - 2005 - Notre Dame Journal of Formal Logic 46 (3):357-371.

Analytics

Added to PP
2020-09-25

Downloads
15 (#941,877)

6 months
8 (#351,446)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

Saturated ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
Reflecting stationary sets.Menachem Magidor - 1982 - Journal of Symbolic Logic 47 (4):755-771.
Some Results in Polychromatic Ramsey Theory.Uri Abraham, James Cummings & Clifford Smyth - 2007 - Journal of Symbolic Logic 72 (3):865 - 896.

View all 7 references / Add more references