Proper forcing, cardinal arithmetic, and uncountable linear orders

Bulletin of Symbolic Logic 11 (1):51-60 (2005)
  Copy   BIBTEX

Abstract

In this paper I will communicate some new consequences of the Proper Forcing Axiom. First, the Bounded Proper Forcing Axiom implies that there is a well ordering of R which is Σ 1 -definable in (H(ω 2 ), ∈). Second, the Proper Forcing Axiom implies that the class of uncountable linear orders has a five element basis. The elements are X, ω 1 , ω 1 * , C, C * where X is any suborder of the reals of size ω 1 and C is any Countryman line. Third, the Proper Forcing Axiom implies the Singular Cardinals Hypothesis at κ unless stationary subsets of S κ + ω reflect. The techniques are expected to be applicable to other open problems concerning the theory of H(ω 2 )

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 92,369

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

Proper forcing and l(ℝ).Itay Neeman & Jindřich Zapletal - 2001 - Journal of Symbolic Logic 66 (2):801-810.
The Proper Forcing Axiom and the Singular Cardinal Hypothesis.Matteo Viale - 2006 - Journal of Symbolic Logic 71 (2):473 - 479.
Co-stationarity of the Ground Model.Natasha Dobrinen & Sy-David Friedman - 2006 - Journal of Symbolic Logic 71 (3):1029 - 1043.
A maximal bounded forcing axiom.David Asperó - 2002 - Journal of Symbolic Logic 67 (1):130-142.
Souslin forcing.Jaime I. Ihoda & Saharon Shelah - 1988 - Journal of Symbolic Logic 53 (4):1188-1207.
Small forcing makes any cardinal superdestructible.Joel David Hamkins - 1998 - Journal of Symbolic Logic 63 (1):51-58.
The bounded proper forcing axiom.Martin Goldstern & Saharon Shelah - 1995 - Journal of Symbolic Logic 60 (1):58-73.

Analytics

Added to PP
2009-01-28

Downloads
44 (#364,044)

6 months
2 (#1,206,230)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations