Abstract:
Effective model theory studies model theoretic notions with an eye towards
issues of computability and effectiveness. We consider two possible starting
points. If the basic objects are taken to be theories, then the appropriate effective
version investigates decidable theories (the set of theorems is computable) and
decidable structures (ones with decidable theories). If the objects of initial
interest are typical mathematical structures, then the starting point is computable
structures. We present an introduction to both of these aspects of effective model
theory organized roughly around the themes of the number and types of models
of theories with particular attention to categoricity (as either a hypothesis or a
conclusion) and the analysis of various computability issues in families of models.