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Splitting number


Author: Tomek Bartoszynski
Journal: Proc. Amer. Math. Soc. 125 (1997), 2141-2145
MSC (1991): Primary 04A20
DOI: https://doi.org/10.1090/S0002-9939-97-03758-1
MathSciNet review: 1372023
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Abstract: We show that it is consistent with ${\operatorname {\mathsf {ZFC}}}$ that every uncountable set can be continuously mapped onto a splitting family.


References [Enhancements On Off] (What's this?)

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  • 3. Jorg Brendle, Haim Judah, and Saharon Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 (1992), 185-199. MR 93k:03048
  • 4. S. H. Hechler, On the existence of certain cofinal subsets of $\omega ^\omega $, Axiomatic Set Theory (T. J. Jech, ed.), Proc. Symp. Pure Math., vol. 13, Amer. Math. Soc., Providence, R.I., 1974, Part 2, pp. 155-173. MR 50:12716
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Additional Information

Tomek Bartoszynski
Affiliation: Department of Mathematics, Boise State University, Boise, Idaho 83725
Email: tomek@math.idbsu.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03758-1
Keywords: Splitting family, cardinal invariants
Received by editor(s): December 11, 1995
Received by editor(s) in revised form: January 18, 1996
Additional Notes: Research partially supported by NSF grant DMS 95-05375
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

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