# DECIDABILITY AND FINITE DIRECT PRODUCTS

• Jeong, Joo-Hee (Topology and Geometry Research Center Kyungpook National University)
• Published : 1998.05.01

#### Abstract

A useful method of proving the finite decidability of an equationally definable class V of algebras (i.e., variety) is to prove the decidability of the class of finite directly indecomposable members of V. The validity of this method relies on the well-known result of Feferman-Vaught: if a class K of first-order structures is decidable, then so is the class {$\prod$$_{i}＜n/ A_{i}$$A_{i}$ $\in$ X (i < n), n $\in$ $\omega$}. In this paper we show that the converse of this does not necessarily hold.d.d.