On uncountable cardinal sequences for superatomic Boolean algebras

Archive for Mathematical Logic 34 (4):257-261 (1995)

Authors
Juan Martínez
Universidad Complutense de Madrid
Abstract
The countable sequences of cardinals which arise as cardinal sequences of superatomic Boolean algebras were characterized by La Grange on the basis of ZFC set theory. However, no similar characterization is available for uncountable cardinal sequences. In this paper we prove the following two consistency results:Ifθ = 〈κ α :α <ω 1〉 is a sequence of infinite cardinals, then there is a cardinal-preserving notion of forcing that changes cardinal exponentiation and forces the existence of a superatomic Boolean algebraB such that θ is the cardinal sequence ofB.Ifκ is an uncountable cardinal such thatκ <κ =κ andθ = 〈κ α :α <κ +〉 is a cardinal sequence such thatκ α ≥κ for everyα <κ + andκ α =κ for everyα <κ + such that cf(α)<κ, then there is a cardinal-preserving notion of forcing that changes cardinal exponentiation and forces the existence of a superatomic Boolean algebraB such that θ is the cardinal sequence ofB
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1007/BF01469382
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 44,386
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

Remarks on Superatomic Boolean Algebras.James E. Baumgartner & Saharon Shelah - 1987 - Annals of Pure and Applied Logic 33 (2):109-129.
Remarks on Superatomic Boolean Algebras.J. E. Baumgartner - 1987 - Annals of Pure and Applied Logic 33 (2):109.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Some Open Questions for Superatomic Boolean Algebras.Juan Carlos Martínez - 2005 - Notre Dame Journal of Formal Logic 46 (3):353-356.
The Number of Openly Generated Boolean Algebras.Stefan Geschke & Saharon Shelah - 2008 - Journal of Symbolic Logic 73 (1):151-164.
A Superatomic Boolean Algebra with Few Automorphisms.Matatyahu Rubin & Sabine Koppelberg - 2001 - Archive for Mathematical Logic 40 (2):125-129.
Club Guessing Sequences and Filters.Tetsuya Ishiu - 2005 - Journal of Symbolic Logic 70 (4):1037-1071.
On the Weak Freese–Nation Property of ?(Ω).Sakaé Fuchino, Stefan Geschke & Lajos Soukupe - 2001 - Archive for Mathematical Logic 40 (6):425-435.
Stationary Cardinals.Wenzhi Sun - 1993 - Archive for Mathematical Logic 32 (6):429-442.
A Cardinal Pattern Inspired by AD.Arthur W. Apter - 1996 - Mathematical Logic Quarterly 42 (1):211-218.
The Tree Property and the Failure of SCH at Uncountable Cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.
MRP , Tree Properties and Square Principles.Remi Strullu - 2011 - Journal of Symbolic Logic 76 (4):1441-1452.

Analytics

Added to PP index
2013-11-23

Total views
9 ( #783,908 of 2,271,753 )

Recent downloads (6 months)
1 ( #823,834 of 2,271,753 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature