## Journal of Symbolic Logic

### On Models with Power-Like Ordering

Saharon Shelah

#### Abstract

We prove here theorems of the form: if $T$ has a model $M$ in which $P_1 (M)$ is $\kappa_1$-like ordered, $P_2(M)$ is $\kappa_2$-like ordered $\ldots$, and $Q_1 (M)$ if of power $\lambda_1, \ldots$, then $T$ has a model $N$ in which $P_1(M)$ is $\kappa_1'$-like ordered $\ldots, Q_1(N)$ is of power $\lambda_1,\ldots$. (In this article $\kappa$ is a strong-limit singular cardinal, and $\kappa'$ is a singular cardinal.) We also sometimes add the condition that $M, N$ omits some types. The results are seemingly the best possible, i.e. according to our knowledge about $n$-cardinal problems (or, more precisely, a certain variant of them).

#### Article information

Source
J. Symbolic Logic, Volume 37, Issue 2 (1972), 247-267.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183738224

Mathematical Reviews number (MathSciNet)
MR446955

Zentralblatt MATH identifier
0273.02036

JSTOR