Mikhail Yakovlevich Suslin

Mikhail Suslin

Mikhail Yakovlevich Suslin (Russian: Михаи́л Я́ковлевич Су́слин; Krasavka, Saratov Oblast, November 15, 1894 – 21 October 1919, Krasavka) (sometimes transliterated Souslin) was a Russian mathematician who made major contributions to the fields of general topology and descriptive set theory.

His name is especially associated to Suslin's problem, a question relating to totally ordered sets that was eventually found to be independent of the standard system of set-theoretic axioms, ZFC.

He contributed greatly to the theory of analytic sets, sometimes called after him, a kind of a set of reals which is definable via trees. In fact, while he was a research student of Nikolai Luzin (in 1917) he found an error in an argument of Lebesgue, who believed he had proved that for any Borel set in $\R^2$, the projection onto the real axis was also a Borel set.

Suslin died of typhus in the 1919 Moscow epidemic following the Russian Civil War.

Publications

Suslin only published one paper during his life: a 4 page note.

• Souslin, M. Ya. (1917), "Sur un définition des ensembles measurables B sans nombres transfinis", C.R. Acad. Sci. Paris 164: 88–91
• Souslin, M. (1920), "Problème 3" (PDF), Fundamenta Mathematicae 1: 223
• Souslin, M. Ya. (1923), Kuratowski, C., ed., "Sur un corps dénombrable de nombres réels", Fundamenta math. (in French) 4: 311–315, JFM 49.0147.03

See also

1.  A Suslin algebra is a Boolean algebra that is complete, atomless, countably distributive, and satisfies the countable chain condition

2.  A Suslin cardinal is a cardinal λ such that there exists a set P ⊂ 2^ω such that P is λ-Suslin but P is not λ'-Suslin for any λ' < λ.

3.  The Suslin hypothesis says that Suslin lines do not exist

4.  A Suslin line is a complete dense unbounded totally ordered set satisfying the countable chain condition

5.  The Suslin number is the supremum of the cardinalities of families of disjoint open non-empty sets

6.  The Suslin operation, usually denoted by A, is an operation that constructs a set from a Suslin scheme

7.  The Suslin problem asks whether Suslin lines exist

8.  The Suslin property states that there is no uncountable family of pairwise disjoint non-empty open subsets

9.  A Suslin representation of a set of reals is a tree whose projection is that set of reals

10.  A Suslin scheme is a function with domain the finite sequences of positive integers

11.  A Suslin set is a set that is the image of a tree under a certain projection

12.  A Suslin space is the image of a Polish space under a continuous mapping

13.  A Suslin subset is a subset that is the image of a tree under a certain projection

14.  The Suslin theorem about analytic sets states that a set that is analytic and coanalytic is Borel

15.  A Suslin tree is a tree of height ω₁ such that every branch and every antichain is at most countable.

References

• Igoshin, V. I. (1996), "A short biography of Mikhail Yakovlevich Suslin", Russ. Math. Surv. 51 (3): 371–383, doi:10.1070/RM1996v051n03ABEH002905
• Akihiro Kanamori, Tenenbaum and Set theory (PDF), p. 2
• Mikhail Yakovlevich Suslin at the Mathematics Genealogy Project
• O'Connor, John J.; Robertson, Edmund F., "Mikhail Yakovlevich Suslin", MacTutor History of Mathematics archive, University of St Andrews.