The character of in first countable spaces
Author:
William G. Fleissner
Journal:
Proc. Amer. Math. Soc. 62 (1977), 149155
MSC:
Primary 54A25; Secondary 04A20
MathSciNet review:
0438272
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Abstract 
References 
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Additional Information
Abstract: We define a cardinal function , where P and Q are properties of topological spaces. We show that it is consistent and independent that .
 [D]
K. Devlin, Aspects of constructibility, Lecture Notes in Math., vol. 354, SpringerVerlag, Berlin and New York, 1973. MR 0376351 (51:12527)
 [D']
, Kurepa's hypothesis and the continuum, Fund. Math. 89 (1975), 2331. (See Added in Proof, p. 30.) MR 0398826 (53:2677)
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W. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294298. MR 50 #14682. MR 0362240 (50:14682)
 [F']
, A normal collectionwise Hausdorff, not collectionwise normal space, General Topology and Appl. 6 (1976), 5774. MR 0391032 (52:11854)
 [H]
S. Hechler, On the existence of certain cofinal subsets of , Proc. Sympos. Pure Math., vol. 13, part 2, Amer. Math. Soc., Providence, R. I., 1974, pp. 155173. MR 50 #12716. MR 0360266 (50:12716)
 [J]
T. Jech, Trees, J. Symbolic Logic 36 (1971), 114. MR 44 #1560. MR 0284331 (44:1560)
 [Ju]
I. Juhász, Consistency results in topology, Logic Handbook (to appear).
 [JW]
I. Juhász and W. Weiss, On a problem of Sikorski, Fund. Math. (to appear) MR 509548 (80g:54006)
 [M]
W. Mitchell, Aronszajn trees and the independence of the transfer property, Ann. Math. Logic 5 (1972), 2146. MR 47 #1612. MR 0313057 (47:1612)
 [R]
M. E. Rudin, Lectures on set theoretic topology, CBMS Regional Conf. Ser. in Math., no. 23, Amer. Math. Soc., Providence, R.I., 1975. MR 51 #4128. MR 0367886 (51:4128)
 [Sh]
S. Shelah, Decomposing uncountable squares into countably many chains (to appear).
 [S]
J. H. Silver, The independence of Kurepa's conjecture and twocardinal conjectures in model theory, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 383390. MR 43 #3112.
 [D]
 K. Devlin, Aspects of constructibility, Lecture Notes in Math., vol. 354, SpringerVerlag, Berlin and New York, 1973. MR 0376351 (51:12527)
 [D']
 , Kurepa's hypothesis and the continuum, Fund. Math. 89 (1975), 2331. (See Added in Proof, p. 30.) MR 0398826 (53:2677)
 [F]
 W. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294298. MR 50 #14682. MR 0362240 (50:14682)
 [F']
 , A normal collectionwise Hausdorff, not collectionwise normal space, General Topology and Appl. 6 (1976), 5774. MR 0391032 (52:11854)
 [H]
 S. Hechler, On the existence of certain cofinal subsets of , Proc. Sympos. Pure Math., vol. 13, part 2, Amer. Math. Soc., Providence, R. I., 1974, pp. 155173. MR 50 #12716. MR 0360266 (50:12716)
 [J]
 T. Jech, Trees, J. Symbolic Logic 36 (1971), 114. MR 44 #1560. MR 0284331 (44:1560)
 [Ju]
 I. Juhász, Consistency results in topology, Logic Handbook (to appear).
 [JW]
 I. Juhász and W. Weiss, On a problem of Sikorski, Fund. Math. (to appear) MR 509548 (80g:54006)
 [M]
 W. Mitchell, Aronszajn trees and the independence of the transfer property, Ann. Math. Logic 5 (1972), 2146. MR 47 #1612. MR 0313057 (47:1612)
 [R]
 M. E. Rudin, Lectures on set theoretic topology, CBMS Regional Conf. Ser. in Math., no. 23, Amer. Math. Soc., Providence, R.I., 1975. MR 51 #4128. MR 0367886 (51:4128)
 [Sh]
 S. Shelah, Decomposing uncountable squares into countably many chains (to appear).
 [S]
 J. H. Silver, The independence of Kurepa's conjecture and twocardinal conjectures in model theory, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 383390. MR 43 #3112.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197704382727
PII:
S 00029939(1977)04382727
Keywords:
Cardinal functions in topology,
diamond plus,
Kurepa's hypothesis
Article copyright:
© Copyright 1977
American Mathematical Society
