Keeping additivity of the null ideal small
Author: Jindrich Zapletal
Journal: Proc. Amer. Math. Soc. 125 (1997), 2443-2451
MSC (1991): Primary 03E35, 03E50
MathSciNet review: 1389541
Full-text PDF Free Access
Abstract: We shall show that various statements are consistent with additivity of the null ideal equal to for example, ``all branchless trees of size are special'', (S) conjecture and ``there are only five cofinal types of directed posets of size ''.
- [B] Tomek Bartoszyński, Additivity of measure implies additivity of category, Trans. Amer. Math. Soc. 281 (1984), no. 1, 209–213. MR 719666, https://doi.org/10.1090/S0002-9947-1984-0719666-7
- [BJ] Tomek Bartoszyński and Haim Judah, Set theory, A K Peters, Ltd., Wellesley, MA, 1995. On the structure of the real line. MR 1350295
- [J] Thomas Jech, Set theory, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. Pure and Applied Mathematics. MR 506523
- [JS] 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, https://doi.org/10.2307/2274464
- [RS] Jean Raisonnier and Jacques Stern, The strength of measurability hypotheses, Israel J. Math. 50 (1985), no. 4, 337–349. MR 800191, https://doi.org/10.1007/BF02759764
- [Tr] J. K. Truss, Connections between different amoeba algebras, Fund. Math. 130 (1988), no. 2, 137–155. MR 963793
- [S] Saharon Shelah, Proper forcing, Lecture Notes in Mathematics, vol. 940, Springer-Verlag, Berlin-New York, 1982. MR 675955
- [SZ] S. Shelah and J. Zapletal, Embeddings of Cohen algebras, Adv. Math. (to appear).
- [T1] Stevo Todorčević, Directed sets and cofinal types, Trans. Amer. Math. Soc. 290 (1985), no. 2, 711–723. MR 792822, https://doi.org/10.1090/S0002-9947-1985-0792822-9
- [T2] Stevo Todorčević, Partition problems in topology, Contemporary Mathematics, vol. 84, American Mathematical Society, Providence, RI, 1989. MR 980949
- [T3] -, A classification of transitive relations on , preprint, 1995.
- T. Bartoszinski, Additivity of measure implies additivity for category, Trans. Amer. Math. Soc. 281 (1984), 209-213. MR 85b:03083
- T. Bartoszynski and H. Judah, Set theory. On the structure of the real line, A K Peters, Wellesley, Massachusets, 1995. MR 96k:03002
- T. Jech, Set Theory, Academic Press, New York, 1978. MR 80a:03062
- H. Judah and S. Shelah, The Kunen-Miller chart, Jour. Symbolic Logic 55 (1990), 909-927. MR 91g:03097
- J. Raisonnier and J. Stern, The strength of measurability hypothesis, Israel Jour. Math. 50 (1985), 337-349. MR 87d:03129
- J. Truss, Connection between different amoeba algebras, Fund. Math. 130 (1988), 137-155. MR 90h:03036
- S. Shelah, Proper Forcing, Springer-Verlag, New York, 1982. MR 84h:03002
- S. Shelah and J. Zapletal, Embeddings of Cohen algebras, Adv. Math. (to appear).
- S. Todorcevic, Directed sets and cofinal types, Trans. Amer. Math. Soc. 290 (1985), 711-723. MR 87a:03084
- -, Partition problems in topology, Amer. Math. Soc., Providence, 1989. MR 90d:04001
- -, A classification of transitive relations on , preprint, 1995.
Affiliation: M. S. R. I., 1000 Centennial Drive, Berkeley, California 94720
Address at time of publication: Mailcode 253-37, California Institute of Technology, Pasadena, California 91125
Email: email@example.com, firstname.lastname@example.org
Received by editor(s): November 8, 1995
Received by editor(s) in revised form: February 26, 1996
Additional Notes: Research at MSRI partially supported by NSF grant # DMS 9022140. The author wishes to thank Itay Neeman for asking the original inspiring question.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society