<div class="csl-bib-body">
<div class="csl-entry">Gonzalez, D., & Rossegger, D. (2024). Scott sentence complexities of linear orderings. <i>Journal of Symbolic Logic</i>. https://doi.org/10.34726/7779</div>
</div>
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dc.identifier.issn
0022-4812
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/206475
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dc.identifier.uri
https://doi.org/10.34726/7779
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dc.description.abstract
We study possible Scott sentence complexities of linear orderings using two approaches. First, we investigate the effect of the Friedman–Stanley embedding on Scott sentence complexity and show that it only preserves Πinα complexities. We then take a more direct approach and exhibit linear orderings of all Scott sentence complexities except Σin3 and Σinλ+1 for λ a limit ordinal. We show that the former cannot be the Scott sentence complexity of a linear ordering. In the process we develop new techniques which appear to be helpful to calculate the Scott sentence complexities of structures.
en
dc.description.sponsorship
European Commission
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dc.language.iso
en
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dc.publisher
CAMBRIDGE UNIV PRESS
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dc.relation.ispartof
Journal of Symbolic Logic
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Scott sentence
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dc.subject
Scott sentence complexity
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dc.subject
Scott rank
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dc.subject
linear orders
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dc.subject
linear orderings
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dc.subject
total orders
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dc.subject
infinitary logic
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dc.subject
computable structures
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dc.title
Scott sentence complexities of linear orderings
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dc.type
Article
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dc.type
Artikel
de
dc.rights.license
Urheberrechtsschutz
de
dc.rights.license
In Copyright
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dc.identifier.doi
10.34726/7779
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dc.contributor.affiliation
University of California, Berkeley, United States of America (the)
