## Journal of Symbolic Logic

### Cardinal Preserving Ideals

#### Abstract

We give some general criteria, when $\kappa$-complete forcing preserves largeness properties-like $\kappa$-presaturation of normal ideals on $\lambda$ (even when they concentrate on small cofinalities). Then we quite accurately obtain the consistency strength "NS$_\lambda$ is $\aleph_1$-preserving". for $\lambda$ > $\aleph_2$.

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 4 (1999), 1527-1551.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745935

Mathematical Reviews number (MathSciNet)
MR1780068

Zentralblatt MATH identifier
0946.03060

JSTOR

#### Citation

Gitik, Moti; Shelah, Saharon. Cardinal Preserving Ideals. J. Symbolic Logic 64 (1999), no. 4, 1527--1551. https://projecteuclid.org/euclid.jsl/1183745935