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 |
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