Random models and the Gödel case of the decision problem
Yuri G. Gurevich, Saharon Shelah · Journal of Symbolic Logic · 1983
Abstract In a paper of 1933 Gödel proved that every satisfiable first-order ∀ 2 ∃* 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 ∀ 2 ∃* sentence.