Article

Full entry | PDF   (0.2 MB)
Keywords:
cardinal invariants of the continuum; splitting number; open splitting number; reaping number; $\sigma$-reaping number; Cicho'n's diagram; Hechler forcing; finite support iteration
Summary:
We prove several results on some cardinal invariants of the continuum which are closely related to either the splitting number $\mathfrak s$ or its dual, the reaping number $\mathfrak r$.
References:
[Ba] Bartoszyński T.: Combinatorial aspects of measure and category. Fundamenta Mathematicae 127 (1987), 225-239. MR 0917147
[BJ] Bartoszyński T., Judah H.: Set Theory. On the Structure of the Real Line. A.K. Peters, Wellesley, Massachusetts, 1995. MR 1350295
[Br] Brendle J.: Mob families and mad families. Archive for Mathematical Logic, to appear. MR 1619601 | Zbl 0905.03034
[Br 1] Brendle J.: Dow's principle and Q-sets. Canadian Math. Bull., to appear. MR 1695894 | Zbl 0933.03059
[BS] Brendle J., Shelah S.: Evasion and prediction II. Journal of the London Mathematical Society 53 (1996), 19-27. MR 1362683 | Zbl 0854.03045
[KW] Kamburelis A., Wȩglorz B.: Splittings. Archive for Mathematical Logic 35 (1996), 263-277. MR 1390805
[Le] Leathrum T.: A special class of almost disjoint families. Journal of Symbolic Logic 60 (1995), 879-891. MR 1348999 | Zbl 0835.03014
[Mi] Miller A.: Some properties of measure and category. Transactions of the American Mathematical Society 266 (1981), 93-114 and 271 (1982), 347-348. MR 0613787 | Zbl 0472.03040
[Mi 1] Miller A.: A characterization of the least cardinal for which the Baire category theorem fails. Proceedings of the American Mathematical Society 86 (1982), 498-502. MR 0671224 | Zbl 0506.03012
[Sh] Shelah S.: Advances in cardinal arithmetic. Finite and infinite combinatorics in sets and logic (N.W. Sauer, R.E. Woodrow and B. Sands, eds.), Kluwer, Dordrecht, 1993, pp.355-383. MR 1261217 | Zbl 0844.03028
[vD] van Douwen E.K.: The integers and topology. Handbook of Set-theoretic Topology (K. Kunen and J.E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp.111-167. MR 0776619 | Zbl 0561.54004
[Va] Vaughan J.: Small uncountable cardinals and topology. Open problems in topology (J. van Mill and G. Reed, eds.), North-Holland, Amsterdam, 1990, pp.195-218. MR 1078647
[Vo] Vojtáš P.: Cardinalities of noncentered systems of subsets of $ømega$. Discrete Mathematics 108 (1992), 125-129. MR 1189835

Partner of