Revised Proof of Skolem's Theorem

Abstract

In [N 91], the author intended to present an easy finitary proof of Skolem's Theorem but unfortunately it turned out to contain some serious errors. This corrected version is self-contained and readers' knowledge of [N 91] is not assuJned. Skolem's Theorem is the following statement: In the classical predicate logic, Iet f be a k-ary function symbol not contained in a formula vxl Vx 9yA(xl' . . . k . . . , xh,y)DB. Then Yx Yx gJ'A(X . . xh,y) :) B 1 ' ' ' k l' " is valid if and only ,f