Computable Model Theory

Computability theory formalizes the intuitive concepts of computation and information content. Pure computability studies these notions and how they relate to definability in arithmetic and set theory. Applied computability examines other areas of mathematics through the lens of effective processes. Tools from computability can be used to give precise definitions of concepts such as randomness. The workshop focussed on two closely related fields: computable algebra and computable model theory. In computable algebra (and computable mathematics in general) we study the computational complexity of the constructions and objects that we use in mathematics. As mathematicians, we all know that certain objects or constructions we deal with are more complicated than others, or maybe equivalent in some sense to others. In computable algebra we use the tools of computability theory to give precise meaning to these intuitions. For instance, we can state and prove a theorem that says that building a maximal ideal in a commutative ring is more difficult than building a prime ideal. The motivations to measure the complexity of mathematics come from two sides. On one side is the foundations of mathematics, with the objective of understanding what type of computational assumptions do we make in regular mathematical practice. On the