The Weak Vopênka Principle for definable classes of structures

We give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures ( WVP ), in accordance with the complexity of their definition, and we determine the large-cardinal strength of each level. Thus, in particular, we show that WVP for $\Sigma_2$-definable cl...

Full description

Bibliographic Details
Authors: Bagaria, Joan, Wilson, Trevor M.
Format: article
Status:Published version
Publication Date:2023
Country:España
Institution:Universidad de Barcelona
Repository:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/217385
Online Access:https://hdl.handle.net/2445/217385
Access Level:Open access
Keyword:Nombres cardinals
Categories (Matemàtica)
Teoria de conjunts
Cardinal numbers
Categories (Mathematics)
Set theory
id ES_02a6882de2ff3dccf94cbf449edcb6d8
oai_identifier_str oai:diposit.ub.edu:2445/217385
network_acronym_str ES
network_name_str España
repository_id_str
spelling The Weak Vopênka Principle for definable classes of structuresBagaria, JoanWilson, Trevor M.Nombres cardinalsCategories (Matemàtica)Teoria de conjuntsCardinal numbersCategories (Mathematics)Set theoryWe give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures ( WVP ), in accordance with the complexity of their definition, and we determine the large-cardinal strength of each level. Thus, in particular, we show that WVP for $\Sigma_2$-definable classes is equivalent to the existence of a strong cardinal. The main theorem (Theorem 5.11) shows, more generally, that WVP for $\Sigma_n$-definable classes is equivalent to the existence of a $\Sigma_n$-strong cardinal (Definition 5.1). Hence, WVP is equivalent to the existence of a $\Sigma_n$-strong cardinal for all $n<\omega$.Association for Symbolic Logic.2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/217385Articles publicats en revistes (Matemàtiques i Informàtica)reponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglésReproducció del document publicat a: https://doi.org/10.1017/jsl.2022.42Journal of Symbolic Logic, 2023, vol. 88, num.1https://doi.org/10.1017/jsl.2022.42(c) Association for Symbolic Logic., 2023info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/2173852026-05-27T06:46:51Z
dc.title.none.fl_str_mv The Weak Vopênka Principle for definable classes of structures
title The Weak Vopênka Principle for definable classes of structures
spellingShingle The Weak Vopênka Principle for definable classes of structures
Bagaria, Joan
Nombres cardinals
Categories (Matemàtica)
Teoria de conjunts
Cardinal numbers
Categories (Mathematics)
Set theory
title_short The Weak Vopênka Principle for definable classes of structures
title_full The Weak Vopênka Principle for definable classes of structures
title_fullStr The Weak Vopênka Principle for definable classes of structures
title_full_unstemmed The Weak Vopênka Principle for definable classes of structures
title_sort The Weak Vopênka Principle for definable classes of structures
dc.creator.none.fl_str_mv Bagaria, Joan
Wilson, Trevor M.
author Bagaria, Joan
author_facet Bagaria, Joan
Wilson, Trevor M.
author_role author
author2 Wilson, Trevor M.
author2_role author
dc.subject.none.fl_str_mv Nombres cardinals
Categories (Matemàtica)
Teoria de conjunts
Cardinal numbers
Categories (Mathematics)
Set theory
topic Nombres cardinals
Categories (Matemàtica)
Teoria de conjunts
Cardinal numbers
Categories (Mathematics)
Set theory
description We give a level-by-level analysis of the Weak Vopěnka Principle for definable classes of relational structures ( WVP ), in accordance with the complexity of their definition, and we determine the large-cardinal strength of each level. Thus, in particular, we show that WVP for $\Sigma_2$-definable classes is equivalent to the existence of a strong cardinal. The main theorem (Theorem 5.11) shows, more generally, that WVP for $\Sigma_n$-definable classes is equivalent to the existence of a $\Sigma_n$-strong cardinal (Definition 5.1). Hence, WVP is equivalent to the existence of a $\Sigma_n$-strong cardinal for all $n<\omega$.
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/217385
url https://hdl.handle.net/2445/217385
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv Reproducció del document publicat a: https://doi.org/10.1017/jsl.2022.42
Journal of Symbolic Logic, 2023, vol. 88, num.1
https://doi.org/10.1017/jsl.2022.42
dc.rights.none.fl_str_mv (c) Association for Symbolic Logic., 2023
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Association for Symbolic Logic., 2023
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Association for Symbolic Logic.
publisher.none.fl_str_mv Association for Symbolic Logic.
dc.source.none.fl_str_mv Articles publicats en revistes (Matemàtiques i Informàtica)
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869402669438730240
score 15,81155

Similar Items