Notions around tree property 1

Annals of Pure and Applied Logic 162 (9):698-709 (2011)

Abstract
In this paper, we study the notions related to tree property 1 , or, equivalently, SOP2. Among others, we supply a type-counting criterion for TP1 and show the equivalence of TP1 and k- TP1. Then we introduce the notions of weak k- TP1 for k≥2, and also supply type-counting criteria for those. We do not know whether weak k- TP1 implies TP1, but at least we prove that each weak k- TP1 implies SOP1. Our generalization of the tree-indiscernibility results in Džamonja and Shelah [5] is crucially used throughout the paper
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1016/j.apal.2011.02.001
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: 40,665
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

Simple Theories.Byunghan Kim & Anand Pillay - 1996 - Annals of Pure and Applied Logic 88 (2):149-164.
Characterizing Rosy Theories.Clifton Ealy & Alf Onshuus - 2007 - Journal of Symbolic Logic 72 (3):919 - 940.
Toward Classifying Unstable Theories.Saharon Shelah - 1996 - Annals of Pure and Applied Logic 80 (3):229-255.
Simple Unstable Theories.Saharon Shelah - 1980 - Annals of Pure and Applied Logic 19 (3):177.
On ◁∗-Maximality.Mirna Džamonja & Saharon Shelah - 2004 - Annals of Pure and Applied Logic 125 (1-3):119-158.

View all 10 references / Add more references

Citations of this work BETA

Theories Without the Tree Property of the Second Kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
On the Existence of Indiscernible Trees.Kota Takeuchi & Akito Tsuboi - 2012 - Annals of Pure and Applied Logic 163 (12):1891-1902.
Dense Codense Predicates and the NTP2.Alexander Berenstein & Hyeung-Joon Kim - 2016 - Mathematical Logic Quarterly 62 (1-2):16-24.
An Axiomatic Approach to Free Amalgamation.Gabriel Conant - 2017 - Journal of Symbolic Logic 82 (2):648-671.
Tree Indiscernibilities, Revisited.Byunghan Kim, Hyeung-Joon Kim & Lynn Scow - 2014 - Archive for Mathematical Logic 53 (1-2):211-232.

View all 9 citations / Add more citations

Similar books and articles

On the Consistency of the Definable Tree Property on ℵ.Amir Leshem - 2000 - Journal of Symbolic Logic 65 (3):1204 - 1214.
The Tree Property at א Ω+2.Sy-David Friedman & Ajdin Halilović - 2011 - Journal of Symbolic Logic 76 (2):477 - 490.
On Iterating Semiproper Preorders.Tadatoshi Miyamoto - 2002 - Journal of Symbolic Logic 67 (4):1431-1468.
Can 'Intrinsic' Be Defined Using Only Broadly Logical Notions?Dan Marshall - 2009 - Philosophy and Phenomenological Research 78 (3):646-672.
Creatures on Ω 1 and Weak Diamonds.Heike Mildenberger - 2009 - Journal of Symbolic Logic 74 (1):1-16.
The Tree Property at ℵ Ω+1.Dima Sinapova - 2012 - Journal of Symbolic Logic 77 (1):279-290.
Fragility and Indestructibility of the Tree Property.Spencer Unger - 2012 - Archive for Mathematical Logic 51 (5-6):635-645.
Reals N-Generic Relative to Some Perfect Tree.Bernard A. Anderson - 2008 - Journal of Symbolic Logic 73 (2):401 - 411.
The Tree Property and the Failure of SCH at Uncountable Cofinality.Dima Sinapova - 2012 - Archive for Mathematical Logic 51 (5-6):553-562.

Analytics

Added to PP index
2013-10-27

Total views
18 ( #451,318 of 2,242,758 )

Recent downloads (6 months)
2 ( #815,164 of 2,242,758 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature