Splitting number
HTML articles powered by AMS MathViewer
- by Tomek Bartoszynski
- Proc. Amer. Math. Soc. 125 (1997), 2141-2145
- DOI: https://doi.org/10.1090/S0002-9939-97-03758-1
- PDF | Request permission
Abstract:
We show that it is consistent with ${\operatorname {\mathsf {ZFC}}}$ that every uncountable set can be continuously mapped onto a splitting family.References
- Tomek Bartoszyński and Haim Judah, Set Theory: on the structure of the real line, A.K. Peters, 1995.
- James E. Baumgartner and Peter Dordal, Adjoining dominating functions, J. Symbolic Logic 50 (1985), no. 1, 94–101. MR 780528, DOI 10.2307/2273792
- Jörg Brendle, Haim Judah, and Saharon Shelah, Combinatorial properties of Hechler forcing, Ann. Pure Appl. Logic 58 (1992), no. 3, 185–199. MR 1191940, DOI 10.1016/0168-0072(92)90027-W
- 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
- Jaime I. Ihoda and Saharon Shelah, Souslin forcing, J. Symbolic Logic 53 (1988), no. 4, 1188–1207. MR 973109, DOI 10.2307/2274613
Bibliographic Information
- Tomek Bartoszynski
- Affiliation: Department of Mathematics, Boise State University, Boise, Idaho 83725
- Email: tomek@math.idbsu.edu
- 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
- © Copyright 1997 American Mathematical Society
- 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