## Journal of Symbolic Logic

### Hanf Number of Omitting Type for Simple First-Order Theories

Saharon Shelah

#### Abstract

Let $T$ be a complete countable first-order theory such that every ultrapower of a model of $T$ is saturated. If $T$ has a model omitting a type $p$ in every cardinality $< \beth_\omega,$ then $T$ has a model omitting $p$ in every cardinality. There is also a related theorem, and an example showing the $\beth_\omega$ cannot be improved.

#### Article information

Source
J. Symbolic Logic, Volume 44, Issue 3 (1979), 319-324.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183740428

Mathematical Reviews number (MathSciNet)
MR540663

Zentralblatt MATH identifier
0428.03025

JSTOR