The computable Models of uncountably categorical Theories

The thesis explores computable model theory, merging model-theoretic concepts with recursion theory. It begins with a review of key model-theoretic principles, particularly the Baldwin-Lachlan theorem on uncountably categorical theories, before delving into recursion theory and the priority method. The core focus is on the recursive spectrum of uncountably categorical theories, examining which models possess computable presentations. This comprehensive and well-explained work serves as an accessible introduction for logicians interested in this active research area.