Structure theorems for o-minimal expansions of groups
Autor(a) principal: | |
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Data de Publicação: | 2000 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.2/2755 |
Resumo: | Let R be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) R is semi-bounded, (2) R has no poles, (3) R cannot define a real closed field with domain R and order <, (4) R is eventually linear and (5) every R-definable set is a finite union of cones. As a corollary we get that Th(R) has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations, bounded R-definable sets and a symbol for each definable endomorphism of the group (R,0,+). |
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Structure theorems for o-minimal expansions of groupsO-minimal structuresStructure theoremsLet R be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) R is semi-bounded, (2) R has no poles, (3) R cannot define a real closed field with domain R and order <, (4) R is eventually linear and (5) every R-definable set is a finite union of cones. As a corollary we get that Th(R) has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations, bounded R-definable sets and a symbol for each definable endomorphism of the group (R,0,+).ElsevierRepositório AbertoEdmundo, Mário Jorge2014-01-07T21:32:21Z2000-032000-03-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/2755engEdmundo, Mário Jorge - Structure theorems for o-minimal expansions of groups. "Annals of Pure and Applied Logic" [Em linha]. ISSN 0168-0072. Vol. 102, Nº 1-2 (Mar. 2000), p. 1-300168-0072info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:16:41Zoai:repositorioaberto.uab.pt:10400.2/2755Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:44:08.977272Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Structure theorems for o-minimal expansions of groups |
title |
Structure theorems for o-minimal expansions of groups |
spellingShingle |
Structure theorems for o-minimal expansions of groups Edmundo, Mário Jorge O-minimal structures Structure theorems |
title_short |
Structure theorems for o-minimal expansions of groups |
title_full |
Structure theorems for o-minimal expansions of groups |
title_fullStr |
Structure theorems for o-minimal expansions of groups |
title_full_unstemmed |
Structure theorems for o-minimal expansions of groups |
title_sort |
Structure theorems for o-minimal expansions of groups |
author |
Edmundo, Mário Jorge |
author_facet |
Edmundo, Mário Jorge |
author_role |
author |
dc.contributor.none.fl_str_mv |
Repositório Aberto |
dc.contributor.author.fl_str_mv |
Edmundo, Mário Jorge |
dc.subject.por.fl_str_mv |
O-minimal structures Structure theorems |
topic |
O-minimal structures Structure theorems |
description |
Let R be an o-minimal expansion of an ordered group (R,0,1,+,<) with distinguished positive element 1. We first prove that the following are equivalent: (1) R is semi-bounded, (2) R has no poles, (3) R cannot define a real closed field with domain R and order <, (4) R is eventually linear and (5) every R-definable set is a finite union of cones. As a corollary we get that Th(R) has quantifier elimination and universal axiomatization in the language with symbols for the ordered group operations, bounded R-definable sets and a symbol for each definable endomorphism of the group (R,0,+). |
publishDate |
2000 |
dc.date.none.fl_str_mv |
2000-03 2000-03-01T00:00:00Z 2014-01-07T21:32:21Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.2/2755 |
url |
http://hdl.handle.net/10400.2/2755 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Edmundo, Mário Jorge - Structure theorems for o-minimal expansions of groups. "Annals of Pure and Applied Logic" [Em linha]. ISSN 0168-0072. Vol. 102, Nº 1-2 (Mar. 2000), p. 1-30 0168-0072 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
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Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
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1799135010862661632 |