## Journal of Symbolic Logic

### Random Models and the Godel Case of the Decision Problem

#### Abstract

In a paper of 1933 Godel proved that every satisfiable first-order $\forall^2\exists^\ast$ sentence has a finite model. Actually he constructed a finite model in an ingenious and sophisticated way. In this paper we use a simple and straightforward probabilistic argument to establish existence of a finite model of an arbitrary satisfiable $\forall^2\exists^\ast$ sentence.

#### Article information

Source
J. Symbolic Logic, Volume 48, Issue 4 (1983), 1120-1124.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183741419

Mathematical Reviews number (MathSciNet)
MR727799

Zentralblatt MATH identifier
0534.03006

JSTOR