Keeping additivity of the null ideal small

Zapletal, Jindřich

doi:10.1090/S0002-9939-97-03870-7

Keeping additivity of the null ideal small
HTML articles powered by AMS MathViewer

by Jindřich Zapletal PDF

Proc. Amer. Math. Soc. 125 (1997), 2443-2451 Request permission

Abstract:

We shall show that various statements are consistent with additivity of the null ideal equal to $\aleph _{1};$ for example, “all branchless trees of size $\aleph _{1}$ are special”, (S) conjecture and “there are only five cofinal types of directed posets of size $\aleph _{1}$”.

References

Tomek Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), no. 1, 209–213. MR 719666, DOI 10.1090/S0002-9947-1984-0719666-7
Tomek Bartoszyński and Haim Judah, Set theory, A K Peters, Ltd., Wellesley, MA, 1995. On the structure of the real line. MR 1350295
Thomas Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 506523
Haim Judah and Saharon Shelah, The Kunen-Miller chart (Lebesgue measure, the Baire property, Laver reals and preservation theorems for forcing), J. Symbolic Logic 55 (1990), no. 3, 909–927. MR 1071305, DOI 10.2307/2274464
Jean Raisonnier and Jacques Stern, The strength of measurability hypotheses, Israel J. Math. 50 (1985), no. 4, 337–349. MR 800191, DOI 10.1007/BF02759764
J. K. Truss, Connections between different amoeba algebras, Fund. Math. 130 (1988), no. 2, 137–155. MR 963793, DOI 10.4064/fm-130-2-137-155
Saharon Shelah, Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin-New York, 1982. MR 675955
S. Shelah and J. Zapletal, Embeddings of Cohen algebras, Adv. Math. (to appear).
Stevo Todorčević, Directed sets and cofinal types, Trans. Amer. Math. Soc. 290 (1985), no. 2, 711–723. MR 792822, DOI 10.1090/S0002-9947-1985-0792822-9
Stevo Todorčević, Partition problems in topology, Contemporary Mathematics, vol. 84, American Mathematical Society, Providence, RI, 1989. MR 980949, DOI 10.1090/conm/084
—, A classification of transitive relations on $\omega _{1}$, preprint, 1995.