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. The random algebra was studied by von Neumann in 1935, in work later published as von Neumann (1998, p. 253), and random forcing was introduced by Solovay (1970).
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
- Solovay, Robert M. (1970), "A model of set-theory in which every set of reals is Lebesgue measurable", Annals of Mathematics. Second Series, 92: 1–56, ISSN 0003-486X, JSTOR 1970696, MR 0265151
- von Neumann, John (1998) [1960], Continuous geometry, Princeton Landmarks in Mathematics, Princeton University Press, ISBN 978-0-691-05893-1, MR 0120174