Height and width of superatomic Boolean algebras
Author:
Judy Roitman
Journal:
Proc. Amer. Math. Soc. 94 (1985), 914
MSC:
Primary 06E99; Secondary 03E35
MathSciNet review:
781045
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Abstract: CantorBendixson height and width of superatomic Boolean algebras is investigated and it is shown that (1) you don't need a Canadian tree to construct an thinthick superatomic Boolean algebra; (2) can be very large and for all and all uncountable , there are no thinvery tall, thintall, very thinthick, or thinthick superatomic Boolean algebras on .
 [1]
James
E. Baumgartner, Almostdisjoint sets, the dense set problem and the
partition calculus, Ann. Math. Logic 9 (1976),
no. 4, 401–439. MR 0401472
(53 #5299)
 [2]
A.
R. D. Mathias (ed.), Surveys in set theory, London
Mathematical Society Lecture Note Series, vol. 87, Cambridge
University Press, Cambridge, 1983. MR 823774
(86m:03005)
 [3]
George
W. Day, Superatomic Boolean algebras, Pacific J. Math.
23 (1967), 479–489. MR 0221993
(36 #5045)
 [4]
Keith
J. Devlin, Kurepa’s hypothesis and the continuum, Fund.
Math. 89 (1975), no. 1, 23–31. MR 0398826
(53 #2677)
 [5]
Keith
J. Devlin, ℵ₁trees, Ann. Math. Logic
13 (1978), no. 3, 267–330. MR 491861
(80c:03053)
 [6]
I.
Juhász and W.
Weiss, On thintall scattered spaces, Colloq. Math.
40 (1978/79), no. 1, 63–68. MR 529798
(82k:54005)
 [7]
Winfried
Just, Two consistency results concerning thintall Boolean
algebras, Algebra Universalis 20 (1985), no. 2,
135–142. MR
806609 (87c:03101), http://dx.doi.org/10.1007/BF01278592
 [8]
Robert
LaGrange, Concerning the cardinal sequence of a Boolean
algebra, Algebra Universalis 7 (1977), no. 3,
307–312. MR 0441811
(56 #205)
 [9]
William
Mitchell, Aronszajn trees and the independence of the transfer
property, Ann. Math. Logic 5 (1972/73), 21–46.
MR
0313057 (47 #1612)
 [10]
M.
Rajagopalan, A chain compact space which is not strongly
scattered, Israel J. Math. 23 (1976), no. 2,
117–125. MR 0402701
(53 #6517)
 [11]
Stevo
B. Todorčević, Some consequences of
𝑀𝐴+¬𝑤𝐾𝐻, Topology Appl.
12 (1981), no. 2, 187–202. MR 612015
(83b:03060), http://dx.doi.org/10.1016/01668641(81)900201
 [12]
Michael
L. Wage, Almost disjoint sets and Martin’s axiom, J.
Symbolic Logic 44 (1979), no. 3, 313–318. MR 540662
(80j:03079), http://dx.doi.org/10.2307/2273124
 [13]
M. Weese, On the classification of compact scattered spaces (Proc. Conf. on Topology and Measure. III), Part 2, Greifswald, 1982, pp. 347356.
 [14]
, On cardinal sequences of Boolean algebras (to appear).
 [1]
 J. Baumgartner, Almost disjoint sets, the dense set problem, and the partition calculus, Ann. of Math. Logic 10 (1976), 401439. MR 0401472 (53:5299)
 [2]
 , Iterated forcing, Surveys in Set Theory (A. R. D. Mathias, ed.), London Math. Soc. Lecture Note Ser. vol. 87, Cambridge Univ. Press, 1983, 159. MR 823774 (86m:03005)
 [3]
 G. W. Day, Superatomic Boolean algebras, Pacific J. Math. (1967), 479489. MR 0221993 (36:5045)
 [4]
 K. J. Devlin, Kurepa's hypothesis and the continuum, Fund. Math. 139 (1975), 2331. MR 0398826 (53:2677)
 [5]
 , trees, Ann. of Math. Logic 13 (1978), 267330. MR 491861 (80c:03053)
 [6]
 I. Juhász and W. Weiss, On thintall scattered spaces, Colloq. Math. 90 (1978), 6368. MR 529798 (82k:54005)
 [7]
 W. Just, Two consistency results concerning thintall Boolean algebras (to appear). MR 806609 (87c:03101)
 [8]
 R. LaGrange, Concerning the cardinal sequence of a Boolean algebra, Algebra Universalis 7 (1977), 307312. MR 0441811 (56:205)
 [9]
 W. Mitchell, Aronszajn trees and the independence of the transfer property, Ann. of Math. Logic 5 (1972), 2146. MR 0313057 (47:1612)
 [10]
 M. Rajagapolan, A chain compact space which is not strongly scattered, Israel J. Math. 23 (1976), 117125. MR 0402701 (53:6517)
 [11]
 S. B. Todorĉević, Some consequences of , Topology Appl. 12 (1981), 187202. MR 612015 (83b:03060)
 [12]
 M. Wage, Almost disjoint sets and Martin's axiom, J. Symbolic Logic 44 (1979), 313318. MR 540662 (80j:03079)
 [13]
 M. Weese, On the classification of compact scattered spaces (Proc. Conf. on Topology and Measure. III), Part 2, Greifswald, 1982, pp. 347356.
 [14]
 , On cardinal sequences of Boolean algebras (to appear).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198507810450
PII:
S 00029939(1985)07810450
Article copyright:
© Copyright 1985
American Mathematical Society
