Constant expansion of theories and the number of countable models

The present paper is dedicated to the method of constant expansion of a complete theory for studying its number of countable models. This paper aims to rehabilitate the method of constant expansion by demonstrating its continued relevance and its potential for use in counting the number of countable models. The main result reveals that the question of reducing the number of countable models from the continuum to a countable number by a constant expansion of a theory remains unanswered, contrary to previous beliefs.