Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support

The Structure of Countable Boolean Algebras

Jussi Ketonen
Annals of Mathematics
Second Series, Vol. 108, No. 1 (Jul., 1978), pp. 41-89
Published by: Annals of Mathematics
DOI: 10.2307/1970929
Stable URL: http://www.jstor.org/stable/1970929
Page Count: 49
  • Read Online (Free)
  • Subscribe ($19.50)
  • Cite this Item
If you need an accessible version of this item please contact JSTOR User Support
The Structure of Countable Boolean Algebras
Preview not available

Abstract

A structure theory for denumerable Boolean algebras is presented. The isomorphism types of countable Boolean algebras are completely characterized in terms of certain naturally defined invariants. As an application, we show that any countable commutative semigroup can be embedded into the semigroup of the isomorphism types of all countable Boolean algebras under direct product. This solves in particular the cube problem of Tarski.

Page Thumbnails

  • Thumbnail: Page 
[41]
    [41]
  • Thumbnail: Page 
42
    42
  • Thumbnail: Page 
43
    43
  • Thumbnail: Page 
44
    44
  • Thumbnail: Page 
45
    45
  • Thumbnail: Page 
46
    46
  • Thumbnail: Page 
47
    47
  • Thumbnail: Page 
48
    48
  • Thumbnail: Page 
49
    49
  • Thumbnail: Page 
50
    50
  • Thumbnail: Page 
51
    51
  • Thumbnail: Page 
52
    52
  • Thumbnail: Page 
53
    53
  • Thumbnail: Page 
54
    54
  • Thumbnail: Page 
55
    55
  • Thumbnail: Page 
56
    56
  • Thumbnail: Page 
57
    57
  • Thumbnail: Page 
58
    58
  • Thumbnail: Page 
59
    59
  • Thumbnail: Page 
60
    60
  • Thumbnail: Page 
61
    61
  • Thumbnail: Page 
62
    62
  • Thumbnail: Page 
63
    63
  • Thumbnail: Page 
64
    64
  • Thumbnail: Page 
65
    65
  • Thumbnail: Page 
66
    66
  • Thumbnail: Page 
67
    67
  • Thumbnail: Page 
68
    68
  • Thumbnail: Page 
69
    69
  • Thumbnail: Page 
70
    70
  • Thumbnail: Page 
71
    71
  • Thumbnail: Page 
72
    72
  • Thumbnail: Page 
73
    73
  • Thumbnail: Page 
74
    74
  • Thumbnail: Page 
75
    75
  • Thumbnail: Page 
76
    76
  • Thumbnail: Page 
77
    77
  • Thumbnail: Page 
78
    78
  • Thumbnail: Page 
79
    79
  • Thumbnail: Page 
80
    80
  • Thumbnail: Page 
81
    81
  • Thumbnail: Page 
82
    82
  • Thumbnail: Page 
83
    83
  • Thumbnail: Page 
84
    84
  • Thumbnail: Page 
85
    85
  • Thumbnail: Page 
86
    86
  • Thumbnail: Page 
87
    87
  • Thumbnail: Page 
88
    88
  • Thumbnail: Page 
89
    89