Suslin's theorem

In mathematics , several closely related sentences of descriptive set theory are referred to as Suslin's sentence (after Mikhail Jakowlewitsch Suslin ).

• There is an analytical set in that is not a Borel set . ${\displaystyle \mathbb {R} }$

• An analytic set im is a Borel set if and only if its complement is an analytic set. ${\displaystyle \mathbb {R} ^{n}}$

• Every analytic set im is the orthogonal projection of a Borel set im . ${\displaystyle \mathbb {R} ^{n}}$ ${\displaystyle \mathbb {R} ^{n+1}}$

• All analytic sets can be constructed by applying Suslin's operation to the closed set family .

literature

• M.Ya. Suslin: Sur un définition des ensembles measurables B sans nombres transfinis , CR Acad. Sci. Paris 164 (1917), pp. 88-91
• N. Lusin, W. Sierpiński: Sur quelques propriétés des Ensembles (A) , Bull. Intern. Acad. Sci. Cracovie A, 35-48 (1918).

Web links

• Suslin Theorem (Encyclopedia of Mathematics)
• Suslin's Theorem (MathWorld)