Authors: Moore, Justin Tatch
Todorčević, Stevo 
Title: Baumgartner’s isomorphism problem for ℵ2 -dense suborders of R
Journal: Archive for Mathematical Logic
Volume: 56
Issue: 7-8
First page: 1105
Last page: 1114
Issue Date: 1-Nov-2017
Rank: M23
ISSN: 0933-5846
DOI: 10.1007/s00153-017-0549-4
Abstract: 
In this paper we will analyze Baumgartner’s problem asking whether it is consistent that 2ℵ0≥ℵ2 and every pair of ℵ2-dense subsets of R are isomorphic as linear orders. The main result is the isolation of a combinatorial principle (∗ ∗) which is immune to c.c.c. forcing and which in the presence of 2ℵ0≤ℵ2 implies that two ℵ2-dense sets of reals can be forced to be isomorphic via a c.c.c. poset. Also, it will be shown that it is relatively consistent with ZFC that there exists an ℵ2 dense suborder X of R which cannot be embedded into - X in any outer model with the same ℵ2.
Keywords: Linear order | Martin’s Axiom | Real type | ℵ -dense 2
Publisher: Springer Link
Project: NSF, Grant DMS-1262019

Show full item record

SCOPUSTM   
Citations

5
checked on Nov 11, 2024

Page view(s)

20
checked on Nov 11, 2024

Google ScholarTM

Check

Altmetric

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.