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- Suslin_tree abstract "In mathematics, a Suslin tree is a tree of height ω1 such that every branch and every antichain is at most countable. (An antichain is a set of elements such that any two are incomparable.) They are named after Mikhail Yakovlevich Suslin.Every Suslin tree is an Aronszajn tree.The existence of a Suslin tree is logically independent of ZFC, and is equivalent to the existence of a Suslin line (shown by Kurepa (1935)) 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. Jensen (1972) 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.".
- Suslin_tree wikiPageExternalLink 326.
- Suslin_tree wikiPageID "5028195".
- Suslin_tree wikiPageLength "2118".
- Suslin_tree wikiPageOutDegree "14".
- Suslin_tree wikiPageRevisionID "621501329".
- Suslin_tree wikiPageWikiLink Aronszajn_tree.
- Suslin_tree wikiPageWikiLink Axiom_of_constructibility.
- Suslin_tree wikiPageWikiLink Category:Trees_(set_theory).
- Suslin_tree wikiPageWikiLink Continuum_hypothesis.
- Suslin_tree wikiPageWikiLink Diamond_principle.
- Suslin_tree wikiPageWikiLink Kurepa_tree.
- Suslin_tree wikiPageWikiLink Martins_axiom.
- Suslin_tree wikiPageWikiLink Mikhail_Yakovlevich_Suslin.
- Suslin_tree wikiPageWikiLink Suslin_algebra.
- Suslin_tree wikiPageWikiLink Suslins_problem.
- Suslin_tree wikiPageWikiLink Thomas_Jech.
- Suslin_tree wikiPageWikiLink Tree_(set_theory).
- Suslin_tree wikiPageWikiLinkText "Suslin tree".
- Suslin_tree wikiPageUsesTemplate Template:Citation.
- Suslin_tree wikiPageUsesTemplate Template:Harvtxt.
- Suslin_tree wikiPageUsesTemplate Template:Settheory-stub.
- Suslin_tree subject Category:Trees_(set_theory).
- Suslin_tree hypernym Tree.
- Suslin_tree type Plant.
- Suslin_tree comment "In mathematics, a Suslin tree is a tree of height ω1 such that every branch and every antichain is at most countable. (An antichain is a set of elements such that any two are incomparable.) They are named after Mikhail Yakovlevich Suslin.Every Suslin tree is an Aronszajn tree.The existence of a Suslin tree is logically independent of ZFC, and is equivalent to the existence of a Suslin line (shown by Kurepa (1935)) or a Suslin algebra.".
- Suslin_tree label "Suslin tree".
- Suslin_tree sameAs Q7649127.
- Suslin_tree sameAs m.03m3qf9.
- Suslin_tree sameAs Q7649127.
- Suslin_tree wasDerivedFrom Suslin_tree?oldid=621501329.
- Suslin_tree isPrimaryTopicOf Suslin_tree.