Uncountable superperfect forcing and minimality

&
Annals of Pure and Applied Logic 144 (1-3):73-82 (2006)
  Copy   BIBTEX

Abstract

Uncountable superperfect forcing is tree forcing on regular uncountable cardinals κ with κ<κ=κ, using trees in which the heights of nodes that split along any branch in the tree form a club set, and such that any node in the tree with more than one immediate extension has measure-one-many extensions, where the measure is relative to some κ-complete, nonprincipal normal filter F. This forcing adds a generic of minimal degree if and only if F is κ-saturated

Categories

Keywords

Reprint years

DOI

10.1016/j.apal.2006.05.012

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,612

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

The tree property and the failure of SCH at uncountable cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.
Grigorieff Forcing on Uncountable Cardinals Does Not Add a Generic of Minimal Degree.Brooke M. Andersen & Marcia J. Groszek - 2009 - Notre Dame Journal of Formal Logic 50 (2):195-200.
Semimorasses and nonreflection at singular cardinals.Piotr Koszmider - 1995 - Annals of Pure and Applied Logic 72 (1):1-23.
Clubs on quasi measurable cardinals.Ashutosh Kumar & Saharon Shelah - 2018 - Mathematical Logic Quarterly 64 (1-2):44-48.
More on simple forcing notions and forcings with ideals.M. Gitik & S. Shelah - 1993 - Annals of Pure and Applied Logic 59 (3):219-238.
Aronszajn trees and the successors of a singular cardinal.Spencer Unger - 2013 - Archive for Mathematical Logic 52 (5-6):483-496.
On the Splitting Number at Regular Cardinals.Omer Ben-Neria & Moti Gitik - 2015 - Journal of Symbolic Logic 80 (4):1348-1360.
Forcing closed unbounded subsets of ω2.M. C. Stanley - 2001 - Annals of Pure and Applied Logic 110 (1-3):23-87.
Power Set Modulo Small, the Singular of Uncountable Cofinality.Saharon Shelah - 2007 - Journal of Symbolic Logic 72 (1):226 - 242.
On uncountable cardinal sequences for superatomic Boolean algebras.Juan Carlos Martínez - 1995 - Archive for Mathematical Logic 34 (4):257-261.

Analytics

Added to PP
2013-12-31

Downloads
23 (#160,613)

6 months
12 (#1,086,452)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Regularity properties on the generalized reals.Sy David Friedman, Yurii Khomskii & Vadim Kulikov - 2016 - Annals of Pure and Applied Logic 167 (4):408-430.
A Lifting Argument for the Generalized Grigorieff Forcing.Radek Honzík & Jonathan Verner - 2016 - Notre Dame Journal of Formal Logic 57 (2):221-231.
Perfect tree forcings for singular cardinals.Natasha Dobrinen, Dan Hathaway & Karel Prikry - 2020 - Annals of Pure and Applied Logic 171 (9):102827.

Add more citations

References found in this work

Saturated ideals.Kenneth Kunen - 1978 - Journal of Symbolic Logic 43 (1):65-76.
Cardinal invariants above the continuum.James Cummings & Saharon Shelah - 1995 - Annals of Pure and Applied Logic 75 (3):251-268.
Combinatorics on ideals and forcing with trees.Marcia J. Groszek - 1987 - Journal of Symbolic Logic 52 (3):582-593.

Add more references