In mathematics, Suslin's problem is a question about totally ordered sets posed by Mikhail Yakovlevich Suslin (1920) and published posthumously. It has been shown to be independent of the standard axiomatic system of set theory known as ZFC; Solovay & Tennenbaum (1971) 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 (Suslin 1920)