Some remarks on a question of D. H. Fremlin regarding ε-density

Archive for Mathematical Logic 40 (7):531-540 (2001)
Abstract
We show the relative consistency of ℵ1 satisfying a combinatorial property considered by David Fremlin (in the question DU from his list) in certain choiceless inner models. This is demonstrated by first proving the property is true for Ramsey cardinals. In contrast, we show that in ZFC, no cardinal of uncountable cofinality can satisfy a similar, stronger property. The questions considered by D. H. Fremlin are if families of finite subsets of ω1 satisfying a certain density condition necessarily contain all finite subsets of an infinite subset of ω1, and specifically if this and a stronger property hold under MA + ¬CH. Towards this we show that if MA + ¬CH holds, then for every family ? of ℵ1 many infinite subsets of ω1, one can find a family ? of finite subsets of ω1 which is dense in Fremlins sense, and does not contain all finite subsets of any set in ?.We then pose some open problems related to the question
Keywords Legacy
Categories (categorize this paper)
DOI 10.1007/s001530100090
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: 33,634
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

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Connected Modal Logics.Guram Bezhanishvili & David Gabelaia - 2011 - Archive for Mathematical Logic 50 (3-4):287-317.
Mad Families, Forcing and the Suslin Hypothesis.Miloš S. Kurilić - 2004 - Archive for Mathematical Logic 44 (4):499-512.
Two Consistency Results on Set Mappings.Péter Komjáth & Saharon Shelah - 2000 - Journal of Symbolic Logic 65 (1):333-338.
Ultrafilters Generated by a Closed Set of Functions.Greg Bishop - 1995 - Journal of Symbolic Logic 60 (2):415-430.
Trees and Π 1 1 -Subsets of Ω1 Ω 1.Alan Mekler & Jouko Vaananen - 1993 - Journal of Symbolic Logic 58 (3):1052 - 1070.
{Pi^1_2} -Comprehension and the Property of Ramsey.Christoph Heinatsch - 2009 - Archive for Mathematical Logic 48 (3-4):323-386.
Pseudo-Finite Homogeneïty and Saturation.Jörg Flum & Martin Ziegler - 1999 - Journal of Symbolic Logic 64 (4):1689-1699.
Trees and $Pi^11$-Subsets of $^{Omega_1}Omega1$.Alan Mekler & Jouko Vaananen - 1993 - Journal of Symbolic Logic 58 (3):1052-1070.
Σ 1 1 -Definability at Uncountable Regular Cardinals.Philipp Lücke - 2012 - Journal of Symbolic Logic 77 (3):1011-1046.
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 index
2013-11-23

Total downloads
9 ( #531,400 of 2,260,026 )

Recent downloads (6 months)
2 ( #217,982 of 2,260,026 )

How can I increase my downloads?

Monthly downloads

My notes

Sign in to use this feature