JORGE ALMEIDA
This work was supported, in part, by FCT, the project Praxis/2/2.1/MAT/63/94, and the Department of Mathematics of the University of Tasmania.
Centro de Matemática da Universidade do Porto, P. Gomes Teixeira, 4099-002 Porto, Portugal

Dedicated to Professor John Rhodes on the occasion of his 60th birthday

Received 15 September 1997
Revised 22 December 1998

Recent results related to hyperdecidability and their applications to decidability of semidirect products are reviewed. Hyperdecidability is studied for pseudovarieties of completely simple semigroups as a means of illustrating the kind of techniques that may be used in this area.

AMSC numbers: Primary 20M07, 20M05, Secondary 20M35