{{Short description|Mathematical theory}} In set theory, the '''random algebra''' or '''random real algebra''' is the Boolean algebra of Borel 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 John von Neumann in 1935 (in work later published as {{harvtxt|Neumann|1998|loc=p. 253}}) who showed that it is not isomorphic to the Cantor algebra of Borel sets modulo meager sets. Random forcing was introduced by {{harvtxt|Solovay|1970}}.
==See also== *Random number
==References== {{refbegin}} *{{citation|mr=2768686 |last=Bartoszyński|first= Tomek|author-link= Tomek Bartoszyński |chapter=Invariants of measure and category|title= Handbook of set theory|volume= 2|pages= 491–555|publisher= Springer|year= 2010}} *{{citation|mr=0485358 |last= Bukowský|first= Lev|chapter= Random forcing|title= Set theory and hierarchy theory, V (Proc. Third Conf., Bierutowice, 1976)|pages= 101–117|series= Lecture Notes in Math.|volume= 619|publisher= Springer|place= Berlin|year= 1977}} *{{Citation | last1=Solovay | first1=Robert M. | author1-link=Robert M. Solovay | title=A model of set-theory in which every set of reals is Lebesgue measurable | jstor=1970696 | mr=0265151 | year=1970 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=92 | issue=1 | pages=1–56 | doi=10.2307/1970696}} *{{Citation | last1=Neumann | first1=John von| author1-link=John von Neumann | title=Continuous geometry | orig-date=1960 | url=https://books.google.com/books?id=onE5HncE-HgC | publisher=Princeton University Press | series=Princeton Landmarks in Mathematics | isbn=978-0-691-05893-1 | mr=0120174 | year=1998}} {{refend}}
Category:Boolean algebra Category:Forcing (mathematics)
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