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In mathematics, a Suslin tree is a tree of height ω1 such thatevery branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn tree. The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown by ) or a Suslin algebra. The diamond principle, a consequence of V=L, implies that there is a Suslin tree, and Martin's axiom MA(ℵ1) implies that there are no Suslin trees.

Attributes	Values
rdf:type	plant
rdfs:label	Suslin tree (en) Árvore de Suslin (pt)
rdfs:comment	In mathematics, a Suslin tree is a tree of height ω1 such thatevery branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn tree. The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown by ) or a Suslin algebra. The diamond principle, a consequence of V=L, implies that there is a Suslin tree, and Martin's axiom MA(ℵ1) implies that there are no Suslin trees. (en) Em matemática, uma árvore Suslin é uma árvore de altura ω1 de tal forma que todos os ramos e a anticadeia sejam no máximo contável. A árvore é nomeada em homenagem Toda árvore de Suslin é uma árvore de Aronszajn A existência de uma árvore de Suslin é independente de ZFC, e é equivalente a existência de uma (provador por ) ou a . O Princípio diamante, uma consequência de V=L, implica que existe uma árvore de Suslin, e Axioma de Martin MA(ℵ1) implica que não há nenhuma árvore de Suslin. (pt)
dcterms:subject	Independence results Trees (set theory)
Wikipage page ID	5028195 (xsd:integer)
Wikipage revision ID	1070235027 (xsd:integer)
Link from a Wikipage to another Wikipage	Antichain List of unsolved problems in set theory Independence (mathematical logic) Kurepa tree Thomas Jech Countable set Glossary of set theory Aronszajn tree Independence results Trees (set theory) Successor cardinal Suslin algebra Tree (set theory) Suslin's problem Suslin line Diamond principle Mikhail Suslin Martin's axiom List of statements independent of ZFC First uncountable ordinal V=L Generalized Continuum Hypothesis
Link from a Wikipage to an external page	http://elibrary.matf.bg.ac.rs/handle/123456789/326
sameAs	Suslin tree Suslin tree Suslin tree Suslin tree Suslin tree Suslin tree
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Harvtxt dbt:Isbn dbt:Settheory-stub
has abstract	In mathematics, a Suslin tree is a tree of height ω1 such thatevery branch and every antichain is at most countable. They are named after Mikhail Yakovlevich Suslin. Every Suslin tree is an Aronszajn tree. The existence of a Suslin tree is independent of ZFC, and is equivalent to the existence of a Suslin line (shown by ) or a Suslin algebra. The diamond principle, a consequence of V=L, implies that there is a Suslin tree, and Martin's axiom MA(ℵ1) implies that there are no Suslin trees. More generally, for any infinite cardinal κ, a κ-Suslin tree is a tree of height κ such that every branch and antichain has cardinality less than κ. In particular a Suslin tree is the same as a ω1-Suslin tree. showed that if V=L then there is a κ-Suslin tree for every infinite successor cardinal κ. Whether the Generalized Continuum Hypothesis implies the existence of an ℵ2-Suslin tree, is a longstanding open problem. (en) Em matemática, uma árvore Suslin é uma árvore de altura ω1 de tal forma que todos os ramos e a anticadeia sejam no máximo contável. A árvore é nomeada em homenagem Toda árvore de Suslin é uma árvore de Aronszajn A existência de uma árvore de Suslin é independente de ZFC, e é equivalente a existência de uma (provador por ) ou a . O Princípio diamante, uma consequência de V=L, implica que existe uma árvore de Suslin, e Axioma de Martin MA(ℵ1) implica que não há nenhuma árvore de Suslin. Mais comumente, para qualquer cardinal infini9to κ, uma κ-árvore de Suslin é uma arvore de altura κ tal que toda ramificação e anticorrente tem cardinalidade menor que κ. Em particular, uma arvore de Suslin é o mesmo que uma ω1-árvore de Suslin. mostrou que se V=L, então tem uma κ-árvore de Suslin para cada infinito cardinal sucessor κ. Se a Hipótese do continuum implica na existência de uma ℵ2-árvore de Suslin, é um problema aberto de longa data. (pt)
gold:hypernym	Tree
prov:wasDerivedFrom	wikipedia-en:Suslin_tree?oldid=1070235027&ns=0
page length (characters) of wiki page	2302 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Suslin_tree
is Link from a Wikipage to another Wikipage of	Kurepa tree Glossary of set theory Aronszajn tree Mikhail Suslin Suslin algebra Tree (set theory) Iterated forcing Suslin's problem Richard Laver Diamond principle List of unsolved problems in mathematics Souslin tree
is Wikipage redirect of	Souslin tree
is foaf:primaryTopic of	wikipedia-en:Suslin_tree

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