Abstract

On 6th Autumn Logic School organized by the Section of Logic of the Institute of Philosophy and Sociology Polish Academy of Sciences, T. Prucnal proved that the consequence operation determined by the ring Zp of the integers modulo prime number p, is ¯nitely based in the language h+; ¡; £; 0; 1i of type h2; 1; 2; 0; 0i. Moreover he asked whether it is true in the h+; ¡; £i-reduct of above language. In this paper we give a positive answer to this question. Our terminology and notations are rather standard. For information on the consequence operations we refer the reader to [2] and for a background on the theory of rings to [1]