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dc.contributor.author
Halbeisen, Lorenz
dc.contributor.author
Schumacher, Salome
dc.date.accessioned
2023-06-13T13:48:44Z
dc.date.available
2023-01-04T04:51:24Z
dc.date.available
2023-01-09T12:43:30Z
dc.date.available
2023-06-13T13:48:44Z
dc.date.issued
2023-07
dc.identifier.issn
0933-5846
dc.identifier.issn
1432-0665
dc.identifier.other
10.1007/s00153-022-00860-4
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/589949
dc.identifier.doi
10.3929/ethz-b-000589949
dc.description.abstract
For n∈ω, the weak choice principle RCn is defined as follows: For every infinite set X there is an infinite subset Y⊆X with a choice function on [Y]n:={z⊆Y:|z|=n}. The choice principle C−n states the following: For every infinite family of n-element sets, there is an infinite subfamily G⊆F with a choice function. The choice principles LOC−n and WOC−n are the same as C−n, but we assume that the family F is linearly orderable (for LOC−n) or well-orderable (for WOC−n). In the first part of this paper, for m,n∈ω we will give a full characterization of when the implication RCm⇒WOC−n holds in ZF. We will prove the independence results by using suitable Fraenkel-Mostowski permutation models. In the second part, we will show some generalizations. In particular, we will show that RC5⇒LOC−5 and that RC6⇒C−3, answering two open questions from Halbeisen and Tachtsis (Arch Math Logik 59(5):583–606, 2020). Furthermore, we will show that RC6⇒C−9 and that RC7⇒LOC−7.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
Springer
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
Axiom of Choice
en_US
dc.subject
Weak forms of the Axiom of Choice
en_US
dc.subject
Ramsey Choice
en_US
dc.subject
Partial Choice for infinite families of n-element sets
en_US
dc.subject
Permutation models
en_US
dc.subject
Pincus' transfer theorems
en_US
dc.title
Some implications of Ramsey Choice for families of n-element sets
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2022-12-16
ethz.journal.title
Archive for Mathematical Logic
ethz.journal.volume
62
en_US
ethz.journal.issue
5-6
en_US
ethz.journal.abbreviated
Arch. math. log.
ethz.pages.start
703
en_US
ethz.pages.end
733
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Berlin
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08848 - Halbeisen, Lorenz (Tit.-Prof.) / Halbeisen, Lorenz (Tit.-Prof.)
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02000 - Dep. Mathematik / Dep. of Mathematics::02003 - Mathematik Selbständige Professuren::08848 - Halbeisen, Lorenz (Tit.-Prof.) / Halbeisen, Lorenz (Tit.-Prof.)
ethz.date.deposited
2023-01-04T04:51:27Z
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2023-06-13T13:48:45Z
ethz.rosetta.lastUpdated
2024-02-03T00:05:35Z
ethz.rosetta.versionExported
true
ethz.COinS
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