Adding dominating reals with the random algebra
Authors: Haim Judah and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 119 (1993), 267-273
MSC: Primary 03E40
MathSciNet review: 1152278
Full-text PDF Free Access
Abstract: We show that there are two models such that by forcing with over we add dominating reals. This answers a question of A. Miller.
- [Ba] Tomek Bartoszyński, On covering of real line by null sets, Pacific J. Math. 131 (1988), no. 1, 1–12. MR 917862
- [BJ1] Tomek Bartoszyński, Jaime I. Ihoda, and Saharon Shelah, The cofinality of cardinal invariants related to measure and category, J. Symbolic Logic 54 (1989), no. 3, 719–726. MR 1011163, https://doi.org/10.2307/2274736
- [BJ2] -, Measure and category in set theory: The assymetry (in preparation).
- [JS1] Jaime I. Ihoda and Saharon Shelah, Souslin forcing, J. Symbolic Logic 53 (1988), no. 4, 1188–1207. MR 973109, https://doi.org/10.2307/2274613
- [JS2] Haim Judah and Saharon Shelah, Around random algebra, Arch. Math. Logic 30 (1990), no. 3, 129–138. MR 1080233, https://doi.org/10.1007/BF01621466
- [Ku] Kenneth Kunen, Set theory, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland Publishing Co., Amsterdam, 1983. An introduction to independence proofs; Reprint of the 1980 original. MR 756630
- [Mi] Arnold W. Miller, The Baire category theorem and cardinals of countable cofinality, J. Symbolic Logic 47 (1982), no. 2, 275–288. MR 654788, https://doi.org/10.2307/2273142
- T. Bartoszynski, Covering the real line by measure zero sets, Pacific J. Math. 1 (1988), 1-12. MR 917862 (89e:03078)
- T. Bartoszynski and H. Judah, On cofinality of the smallest covering of the real line by meager sets, J. Symbolic Logic 54 (1989), 719-726. MR 1011163 (90f:03082)
- -, Measure and category in set theory: The assymetry (in preparation).
- H. Judah and S. Shelah, Souslin forcing, J. Symbolic Logic 53 (1988), 1188-1207. MR 973109 (90h:03035)
- -, Around random algebra, Arch. Math. Logic 30 (1990), 128-138. MR 1080233 (91i:03099)
- K. Kunen, Set theory, North-Holland, Amsterdam. MR 756630 (85e:03003)
- A. Miller, Baire theorem and cardinals of countable cofinality, J. Symbolic Logic 47 (1982). MR 654788 (83h:03073)
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03E40
Retrieve articles in all journals with MSC: 03E40