The character of 𝜔₁ in first countable spaces

Fleissner, William G.

doi:10.1090/S0002-9939-1977-0438272-7

The character of $\omega _{1}$ in first countable spaces
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by William G. Fleissner

Proc. Amer. Math. Soc. 62 (1977), 149-155

DOI: https://doi.org/10.1090/S0002-9939-1977-0438272-7

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Abstract:

We define a cardinal function $\chi (P,Q)$, where P and Q are properties of topological spaces. We show that it is consistent and independent that $\chi ({\omega _1},\;{\text {first}}\;{\text {countable}}) = {\omega _1}$.

References

Keith J. Devlin, Aspects of constructibility, Lecture Notes in Mathematics, Vol. 354, Springer-Verlag, Berlin-New York, 1973. MR 0376351, DOI 10.1007/BFb0059290
Keith J. Devlin, Kurepa’s hypothesis and the continuum, Fund. Math. 89 (1975), no. 1, 23–31. MR 398826, DOI 10.4064/fm-89-1-23-31
William Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298. MR 362240, DOI 10.1090/S0002-9939-1974-0362240-4
William G. Fleissner, A normal collectionwise Hausdorff, not collectionwise normal space, General Topology and Appl. 6 (1976), no. 1, 57–64. MR 391032, DOI 10.1016/0016-660X(76)90008-8
Stephen H. Hechler, On the existence of certain cofinal subsets of $^{\omega }\omega$, Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part II, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1974, pp. 155–173. MR 0360266
Thomas J. Jech, Trees, J. Symbolic Logic 36 (1971), 1–14. MR 284331, DOI 10.2307/2271510

Consistency results in topology

I. Juhász and William Weiss, On a problem of Sikorski, Fund. Math. 100 (1978), no. 3, 223–227. MR 509548, DOI 10.4064/fm-100-3-223-227
William Mitchell, Aronszajn trees and the independence of the transfer property, Ann. Math. Logic 5 (1972/73), 21–46. MR 313057, DOI 10.1016/0003-4843(72)90017-4
Mary Ellen Rudin, Lectures on set theoretic topology, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 23, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, R.I., 1975. Expository lectures from the CBMS Regional Conference held at the University of Wyoming, Laramie, Wyo., August 12–16, 1974. MR 0367886, DOI 10.1090/cbms/023

Decomposing uncountable squares into countably many chains

The independence of Kurepa’s conjecture and two-cardinal conjectures in model theory

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