85:). It is isomorphic to the completion of the countable Cantor algebra. (The complete Cantor algebra is sometimes called the Cohen algebra, though "
89:" usually refers to a different type of Boolean algebra.) The complete Cantor algebra was studied by von Neumann in 1935 (later published as (
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on a countable number of generators. Up to isomorphism, this is the only nontrivial
Boolean algebra that is both countable and atomless.
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116:"Weak distributivity, a problem of von Neumann and the mystery of measurability"
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The complete Cantor algebra is the complete
Boolean algebra of
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The countable Cantor algebra is the
Boolean algebra of all
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For the algebras encoding a bijection from an infinite set
93:)), who showed that it is not isomorphic to the
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97:of Borel subsets modulo measure zero sets.
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28:, sometimes called Cantor algebras, see
149:, Princeton Landmarks in Mathematics,
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14:
43:, is one of two closely related
1:
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151:Princeton University Press
121:Bulletin of Symbolic Logic
15:
83:Balcar & Jech 2006
30:Jónsson–Tarski algebra
185:Forcing (mathematics)
77:of the reals modulo
68:free Boolean algebra
146:Continuous geometry
35:In mathematics, a
160:978-0-691-05893-1
141:von Neumann, John
20:onto the product
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108:Balcar, Bohuslav
91:von Neumann 1998
45:Boolean algebras
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190:Boolean algebra
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128:(2): 241–266,
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95:random algebra
66:. This is the
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37:Cantor algebra
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112:Jech, Thomas
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41:Georg Cantor
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79:meager sets
179:Categories
101:References
64:Cantor set
143:(1998) ,
49:countable
114:(2006),
53:complete
51:and one
169:0120174
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60:clopen
47:, one
155:ISBN
181::
165:MR
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81:(
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26:X
24:Ă—
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