Independence results | Order theory

Suslin's problem

In mathematics, Suslin's problem is a question about totally ordered sets posed by Mikhail Yakovlevich Suslin and published posthumously.It has been shown to be independent of the standard axiomatic system of set theory known as ZFC: showed that the statement can neither be proven nor disproven from those axioms, assuming ZF is consistent. (Suslin is also sometimes written with the French transliteration as Souslin, from the Cyrillic Суслин.) Un ensemble ordonné (linéairement) sans sauts ni lacunes et tel que tout ensemble de ses intervalles (contenant plus qu'un élément) n'empiétant pas les uns sur les autres est au plus dénumerable, est-il nécessairement un continue linéaire (ordinaire)?Is a (linearly) ordered set without jumps or gaps and such that every set of its intervals (containing more than one element) not overlapping each other is at most denumerable, necessarily an (ordinary) linear continuum? The original statement of Suslin's problem from (Wikipedia).

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Related pages

Topological space | Set theory | List of statements independent of ZFC | Separable space | Conjecture | Order topology | Limit cardinal | Disjoint sets | Diamond principle | Axiom of constructibility | Regular cardinal | Forcing (mathematics) | Cantor's isomorphism theorem | Independence (mathematical logic) | Inner model | AD+ | Completeness (order theory) | Order isomorphism | Suslin tree | Tree (set theory) | Successor cardinal | Mathematics | Continuum hypothesis | Axiomatic system | Suslin algebra | Axiom of determinacy | Greatest element and least element | Superstrong cardinal | Dense order | Square principle | Countable chain condition | Cardinality | Antichain | Open set | Martin's axiom