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P(R), ordered by homeomorphic embeddability, does not represent all posets of cardinality c2

Abstract:

We prove it to be consistent that there is a poset of cardinality c2 which is not realizable in P(R), ordered by homeomorphic embeddability. This addresses and answers resolutely (and in the negative) the open question of whether there is a ZFC theorem that all posets of cardinality c2 can be represented by subspaces of the real line ordered by homeomorphic embeddability. This question arises from the pioneering work of Banach, Kuratowski and Sierpiński in the area and t...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.topol.2009.03.014

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
More by this author
Institution:
National University of Ireland Galway
Role:
Author
Publisher:
Elsevier Publisher's website
Journal:
Topology and its Applications Journal website
Volume:
156
Issue:
11
Pages:
1943–1945
Publication date:
2009-06-01
DOI:
ISSN:
0166-8641
Language:
English
Keywords:
Subjects:
UUID:
uuid:50c5acec-9b28-4c7a-be5d-82939a3bb866
Local pid:
ora:10782
Deposit date:
2015-03-31

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