## Journal of Symbolic Logic

### Independence Results

Saharon Shelah

#### Abstract

We prove independence results concerning the number of nonisomorphic models (using the $\mathbf{S}$-chain condition and $\mathbf{S}$-properness) and the consistency of "$ZCF + 2^{\aleph_0} = \aleph_2 + \text{there is a universal linear order of power} \aleph_1$". Most of these results were announced in [Sh 4], [Sh 5]. In subsequent papers we shall prove an analog f MA for forcing which does not destroy stationary subsets of $\omega_1$, investigate $\mathscr{D}$-properness for various filters and prove the consistency with G.C.H. of an axiom implying SH (for $\aleph_1$), and connected results.

#### Article information

Source
J. Symbolic Logic, Volume 45, Issue 3 (1980), 563-573.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183740621

Mathematical Reviews number (MathSciNet)
MR583374

Zentralblatt MATH identifier
0451.03017

JSTOR