## Journal of Symbolic Logic

### End Extensions and Numbers of Countable Models

Saharon Shelah

#### Abstract

We prove that every model of $T = \mathrm{Th}(\omega, <, \ldots) (T$ countable) has an end extension; and that every countable theory with an infinite order and Skolem functions has $2^{\mathbf{\aleph}_0}$ nonisomorphic countable models; and that if every model of $T$ has an end extension, then every $|T|$-universal model of $T$ has an end extension definable with parameters.

#### Article information

Source
J. Symbolic Logic, Volume 43, Issue 3 (1978), 550-562.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183740260

Mathematical Reviews number (MathSciNet)
MR503792

Zentralblatt MATH identifier
0412.03043

JSTOR