On the Consistency of Some Partition Theorems for Continuous Colorings, and the Structure of ℵ 1 -Dense Real Order Types

Bulletin of Symbolic Logic 8 (2):303 (2002)

We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ℵ 1 -dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ℵ 1 -dense subsets of R are isomorphic, is consistent. We e.g. prove Con). Let K H , be the set of order types of ℵ 1 -dense homogeneous subsets of R with the relation of embeddability. We prove that for every finite model L , : Con iff L is a distributive lattice. We prove that it is consistent that the Magidor-Malitz language is not countably compact. We deal with the consistency of certain topological partition theorems. E.g. We prove that MA is consistent with the axiom OCA which says: “If X is a second countable space of power ℵ 1 , and { U 0 ,\h.;, U n−1 } is a cover of D ▪ X x X -} x,x> ¦ x ϵ X } consisting of symmetric open sets, then X can be partitioned into { X i \brvbar; i ϵ ω } such that for every i ϵ ω there is l such that D ⊇ U l ”. We also prove that MA+OCA [xrArr] 2 ℵ 0 = ℵ 2
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2693971
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: 39,951
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

Chains and Antichains in P(Ω).James E. Baumgartner - 1980 - Journal of Symbolic Logic 45 (1):85-92.
Compact Extensions of L(Q).Menachem Magidor & Jerome Malitz - 1977 - Annals of Mathematical Logic 11 (2):217--261.

Add more references

Citations of this work BETA

Chain Conditions of Products, and Weakly Compact Cardinals.Assaf Rinot - 2014 - Bulletin of Symbolic Logic 20 (3):293-314,.
Combinatorial Dichotomies in Set Theory.Stevo Todorcevic - 2011 - Bulletin of Symbolic Logic 17 (1):1-72.
Sacks Forcing, Laver Forcing, and Martin's Axiom.Haim Judah, Arnold W. Miller & Saharon Shelah - 1992 - Archive for Mathematical Logic 31 (3):145-161.

View all 21 citations / Add more citations

Similar books and articles

A Dual Open Coloring Axiom.Stefan Geschke - 2006 - Annals of Pure and Applied Logic 140 (1):40-51.
Uniform Continuity Properties of Preference Relations.Douglas S. Bridges - 2008 - Notre Dame Journal of Formal Logic 49 (1):97-106.
On Topological Properties of Ultraproducts of Finite Sets.Gábor Sági & Saharon Shelah - 2005 - Mathematical Logic Quarterly 51 (3):254-257.
Some Results in the Partition Calculus.Albin Lee Jones - 1999 - Dissertation, Dartmouth College
Partition-Theorems for Causal Decision Theories.Jordan Howard Sobel - 1989 - Philosophy of Science 56 (1):70-93.
Two Cardinal Models for Singular Μ.Shimon Garti & Saharon Shelah - 2007 - Mathematical Logic Quarterly 53 (6):636-641.
Simple Monadic Theories and Partition Width.Achim Blumensath - 2011 - Mathematical Logic Quarterly 57 (4):409-431.
Analytic Colorings.Wiesław Kubiś & Saharon Shelah - 2003 - Annals of Pure and Applied Logic 121 (2-3):145-161.
[Omnibus Review].Peter J. Nyikos - 1992 - Journal of Symbolic Logic 57 (2):763-766.
A Theorem and Some Consistency Results in Partition Calculus.Saharon Shelah & Lee Stanley - 1987 - Annals of Pure and Applied Logic 36 (2):119-152.


Added to PP index

Total views
12 ( #604,871 of 2,235,840 )

Recent downloads (6 months)
7 ( #231,609 of 2,235,840 )

How can I increase my downloads?


My notes

Sign in to use this feature