Splitting number

Splitting number
HTML articles powered by AMS MathViewer

by Tomek Bartoszynski PDF

Proc. Amer. Math. Soc. 125 (1997), 2141-2145 Request permission

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