Random algebra

In set theory, the random algebra or random real algebra is the Boolean algebra of measurable sets of the unit interval modulo the ideal of measure zero sets. It is used in random forcing to add random reals to a model of set theory. It was studied by von Neumann in 1935, in work later published as von Neumann (1998, p. 253).

See also

• Cohen algebra of Borel sets modulo meager sets.

References

• Bartoszynski, Tomek (2010), "Invariants of measure and category", Handbook of set theory, vol. 2, Springer, pp. 491–555, MR 2768686
• Bukowský, Lev (1977), "Random forcing", Set theory and hierarchy theory, V (Proc. Third Conf., Bierutowice, 1976), Lecture Notes in Math., vol. 619, Berlin: Springer, pp. 101–117, MR 0485358
• von Neumann, John (1998) [1960], Continuous geometry, Princeton Landmarks in Mathematics, Princeton University Press, ISBN 978-0-691-05893-1, MR 0120174