Archive for Mathematical Logic 58 (5-6):767-785 (2019)

We study two ideals which are naturally associated to independent families. The first of them, denoted \, is characterized by a diagonalization property which allows along a cofinal sequence of stages along a finite support iteration to adjoin a maximal independent family. The second ideal, denoted \\), originates in Shelah’s proof of \ in Shelah, 433–443, 1992). We show that for every independent family \, \\subseteq \mathcal {J}_\mathcal {A}\) and define a class of maximal independent families, to which we refer as densely maximal, for which the two ideals coincide. Building upon the techniques of Shelah we characterize Sacks indestructibility for such families in terms of properties of \\) and devise a countably closed poset which adjoins a Sacks indestructible densely maximal independent family.
Keywords No keywords specified (fix it)
Categories No categories specified
(categorize this paper)
DOI 10.1007/s00153-019-00669-8
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,319
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

Mad Families, Splitting Families and Large Continuum.Jörg Brendle & Vera Fischer - 2011 - Journal of Symbolic Logic 76 (1):198 - 208.
The Spectrum of Independence.Vera Fischer & Saharon Shelah - 2019 - Archive for Mathematical Logic 58 (7-8):877-884.
Con(U>I).Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (6):433-443.

Add more references

Citations of this work BETA

Add more citations

Similar books and articles

Political Ideals.Bertrand Russell - 1917 - Prometheus Books.
Products of Ideals in MV -Algebras.P. L. Belluce, A. Lettieri & S. Sessa - 2001 - Journal of Applied Non-Classical Logics 11 (3-4):341-350.
Monomial Ideals and Independence of IΣ2.Florian Pelupessy - 2017 - Mathematical Logic Quarterly 63 (1-2):59-65.
The Concept of Ideals in Legal Theory.Sanne Taekema - 2003 - Kluwer Law International.
Independence Logic and Abstract Independence Relations.Gianluca Paolini - 2015 - Mathematical Logic Quarterly 61 (3):202-216.
'Ideas' and 'Structure' in the Formation of Independence Ideals.A. D. Smith - 1973 - Philosophy of the Social Sciences 3 (1):19-39.
On Ideals Related to I[Λ].Todd Eisworth - 2005 - Notre Dame Journal of Formal Logic 46 (3):301-307.
Independence of Irrelevant Alternatives Revisited.Susumu Cato - 2014 - Theory and Decision 76 (4):511-527.
Katětov Order on Borel Ideals.Michael Hrušák - 2017 - Archive for Mathematical Logic 56 (7-8):831-847.
Hyper MV -Ideals in Hyper MV -Algebras.Lida Torkzadeh & Afsaneh Ahadpanah - 2010 - Mathematical Logic Quarterly 56 (1):51-62.
Discouraging Results for Ultraimaginary Independence Theory.Itay Ben-Yaacov - 2003 - Journal of Symbolic Logic 68 (3):846-850.


Added to PP index

Total views
13 ( #744,089 of 2,448,668 )

Recent downloads (6 months)
1 ( #447,034 of 2,448,668 )

How can I increase my downloads?


My notes