We will study the question about decidability for Boolean algebras wit
h first elementary characteristic one. The main problem is sufficient
conditions for decidability of Boolean algebras with recursive represe
ntation for extended signature by definable predicates. We will use th
e base definitions on recursive and constructive models from [2, 4-6,
10, 11] but on Boolean algebras from [1, 8]. (C) 1998 Published by Els
evier Science B.V. All rights reserved.