Non-well-founded set theory (original) (raw)

About DBpedia

Em ZFC sem o axioma da regularidade, a possibilidade de infundados conjuntos surgem. Estes conjuntos, se existem, são também chamados hiperconjuntos. Claramente, se A ∈ A, então A é um hiperconjunto. Em 1988, Peter Aczel publicou um trabalho influente, Non-Well-Founded Sets (Conjuntos Não-Bem-Fundados). A teoria dos hiperconjuntos tem sido aplicada à ciência computacional (processamento algébrico e semântica limite), linguística (teoria da situação), e filosofia (trabalho sobre o paradoxo de Liar).

Property Value
dbo:abstract Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. The study of non-well-founded sets was initiated by Dmitry Mirimanoff in a series of papers between 1917 and 1920, in which he formulated the distinction between well-founded and non-well-founded sets; he did not regard well-foundedness as an axiom. Although a number of axiomatic systems of non-well-founded sets were proposed afterwards, they did not find much in the way of applications until Peter Aczel’s in 1988.The theory of non-well-founded sets has been applied in the logical modelling of non-terminating computational processes in computer science (process algebra and ), linguistics and natural language semantics (situation theory), philosophy (work on the Liar Paradox), and in a different setting, non-standard analysis. (en) La théorie des ensembles non bien fondés est une variante de la théorie axiomatique des ensembles qui permet aux ensembles de s'appartenir les uns aux autres sans limite. Autrement dit, c'est une théorie des ensembles qui ne satisfait pas l'axiome de fondation. Plus précisément, dans la théorie des ensembles non bien fondés, l'axiome de fondation de ZFC est remplacé par un axiome impliquant sa négation. L'étude des ensembles non-bien-fondés a été initiée par Demetrius Mirimanoffdans une série d'articles qu'il a publié en français entre 1917 et 1920 et dans lesquels il énonce une distinction entre des suites bien fondées et des suites non bien fondées ; cependant il ne fait pas recours à un axiome de bonne fondation. Alors que plusieurs axiomatiques pour les ensembles non bien fondés ont été proposées par la suite, aucune n'a trouvé d'application jusqu'à ce que Peter Aczel propose sa théorie des hyper-ensembles en 1988. La théorie des ensembles non-bien-fondés permet d'offrir des modèles pour la non-terminaison des calculs de processus en informatique (algèbre de processus), pour la linguistique et pour la sémantique du langage naturel. De plus elle a des applications en philosophie (paradoxe du menteur ) et en analyse non standard. (fr) Em ZFC sem o axioma da regularidade, a possibilidade de infundados conjuntos surgem. Estes conjuntos, se existem, são também chamados hiperconjuntos. Claramente, se A ∈ A, então A é um hiperconjunto. Em 1988, Peter Aczel publicou um trabalho influente, Non-Well-Founded Sets (Conjuntos Não-Bem-Fundados). A teoria dos hiperconjuntos tem sido aplicada à ciência computacional (processamento algébrico e semântica limite), linguística (teoria da situação), e filosofia (trabalho sobre o paradoxo de Liar). (pt)
dbo:wikiPageExternalLink http://www1.maths.leeds.ac.uk/~rathjen/russelle.pdf http://repository.bilkent.edu.tr/bitstream/11693/25955/1/Issues%20in%20commonsense%20set%20theory.pdf http://us.metamath.org/mpegif/ax-reg.html http://tinf2.vub.ac.be/~dvermeir/mirrors/www.cs.bilkent.edu.tr/%257Eakman/jour-papers/air/node8.html https://archive.org/details/nonwellfoundedse0000acze/page/ https://books.google.com/books%3Fid=L3M8DwAAQBAJ https://books.google.com/books%3Fid=TM3AKPYdQVgC https://books.google.com/books%3Fid=TM3AKPYdQVgC&pg=PA186 https://books.google.com/books%3Fid=zbGjAQAAQBAJ http://plato.stanford.edu/entries/nonwellfounded-set-theory/ http://users.auth.gr/~tzouvara/Texfiles.htm/non-well.pdf%7Cyear=2003
dbo:wikiPageID 1091767 (xsd:integer)
dbo:wikiPageLength 11789 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID 1108319949 (xsd:integer)
dbo:wikiPageWikiLink dbr:New_Foundations dbr:Binary_relation dbr:John_von_Neumann dbr:Paul_Bernays dbr:Peter_Aczel dbr:Independence_(mathematical_logic) dbr:Anti-Foundation_Axiom dbr:Ernst_Specker dbr:Liar's_paradox dbr:Liar_Paradox dbr:Logic dbr:Computing dbr:Axiomatic_set_theory dbr:Aczel's_anti-foundation_axiom dbr:Turtles_all_the_way_down dbr:Well-foundedness dbr:Willard_Van_Orman_Quine dbr:Dmitry_Mirimanoff dbr:John_Etchemendy dbr:Jon_Barwise dbr:Linguistics dbr:Situation_theory dbr:Dana_Scott dbr:Alternative_set_theory dbr:Accessible_pointed_graph dbr:Non-standard_analysis dbr:Nonstandard_analysis dbc:Systems_of_set_theory dbr:Bisimulation dbr:ZFC dbc:Wellfoundedness dbc:Self-reference dbr:Axiom dbr:Axiom_of_extensionality dbr:Axiom_of_regularity dbr:Habilitationsschrift dbr:Metamath dbr:Semantics dbr:Von_Neumann_universe dbr:Universal_set dbr:Extensionality dbr:Natural_language dbr:Paul_Finsler dbr:Maurice_Boffa dbr:Well-founded_set dbr:Quine_atom dbr:Process_algebra dbr:Model_(abstract) dbr:Final_semantics dbr:Hyperset_theory dbr:Rieger's_theorem dbr:Superuniversality
dbp:wikiPageUsesTemplate dbt:Set_theory dbt:Citation dbt:Cite_book dbt:Cite_web dbt:Expand_section dbt:Reflist dbt:Sfnp dbt:Short_description dbt:Mathematical_logic
dct:subject dbc:Systems_of_set_theory dbc:Wellfoundedness dbc:Self-reference
gold:hypernym dbr:Variants
rdf:type dbo:MeanOfTransportation yago:Artifact100021939 yago:Instrumentality103575240 yago:Object100002684 yago:PhysicalEntity100001930 yago:System104377057 yago:Whole100003553 yago:WikicatSystemsOfSetTheory
rdfs:comment Em ZFC sem o axioma da regularidade, a possibilidade de infundados conjuntos surgem. Estes conjuntos, se existem, são também chamados hiperconjuntos. Claramente, se A ∈ A, então A é um hiperconjunto. Em 1988, Peter Aczel publicou um trabalho influente, Non-Well-Founded Sets (Conjuntos Não-Bem-Fundados). A teoria dos hiperconjuntos tem sido aplicada à ciência computacional (processamento algébrico e semântica limite), linguística (teoria da situação), e filosofia (trabalho sobre o paradoxo de Liar). (pt) Non-well-founded set theories are variants of axiomatic set theory that allow sets to be elements of themselves and otherwise violate the rule of well-foundedness. In non-well-founded set theories, the foundation axiom of ZFC is replaced by axioms implying its negation. (en) La théorie des ensembles non bien fondés est une variante de la théorie axiomatique des ensembles qui permet aux ensembles de s'appartenir les uns aux autres sans limite. Autrement dit, c'est une théorie des ensembles qui ne satisfait pas l'axiome de fondation. Plus précisément, dans la théorie des ensembles non bien fondés, l'axiome de fondation de ZFC est remplacé par un axiome impliquant sa négation. (fr)
rdfs:label Théorie des ensembles non bien fondés (fr) Non-well-founded set theory (en) Hiperconjunto (pt)
owl:sameAs freebase:Non-well-founded set theory yago-res:Non-well-founded set theory wikidata:Non-well-founded set theory dbpedia-fa:Non-well-founded set theory dbpedia-fr:Non-well-founded set theory dbpedia-pt:Non-well-founded set theory https://global.dbpedia.org/id/4sc3z
prov:wasDerivedFrom wikipedia-en:Non-well-founded_set_theory?oldid=1108319949&ns=0
foaf:isPrimaryTopicOf wikipedia-en:Non-well-founded_set_theory
is dbo:wikiPageRedirects of dbr:Non-well-founded_set dbr:Nonstandard_set_theory dbr:Nonwellfounded_set_theory dbr:Non-wellfounded_set_theory dbr:Non-well-founded_set_theories dbr:Axiom_of_superuniversality dbr:Hyperset
is dbo:wikiPageWikiLink of dbr:Rose_tree dbr:Mostowski_collapse_lemma dbr:New_Foundations dbr:Non-well-founded_set dbr:Nonstandard_set_theory dbr:Nonwellfounded_set_theory dbr:Peter_Aczel dbr:Liar_paradox dbr:General_formal_ontology dbr:Rooted_graph dbr:Coinduction dbr:Constructive_set_theory dbr:Corecursion dbr:Epsilon-induction dbr:Aczel's_anti-foundation_axiom dbr:Dmitry_Mirimanoff dbr:Fuzzy_concept dbr:Jon_Barwise dbr:Self-similarity dbr:Situation_theory dbr:Alternative_set_theory dbr:Finite_set dbr:Non-wellfounded_set_theory dbr:Axiom_of_regularity dbr:Circular_definition dbr:Ordinal_number dbr:Universal_set dbr:Non-well-founded_set_theories dbr:Situation_semantics dbr:Urelement dbr:Paul_Finsler dbr:Revision_theory dbr:Axiom_of_superuniversality dbr:Hyperset
is foaf:primaryTopic of wikipedia-en:Non-well-founded_set_theory