May 9
Michele Bailetti,
Wesleyan University
Notions of maximality in first-order theories
In the classification of complete first-order theories, many dividing lines have been defined in order to understand the complexity and the behavior of some classes of theories. In this talk, using the concept of patterns of consistency and inconsistency, we describe a general framework to study combinatorially defined dividing lines and we introduce a notion of maximal complexity by requesting the presence of all the exhibitable patterns of definable sets. Weakening this notion, we define new properties (Positive Maximality and the $PM^{(k)}$ hierarchy) and prove some results about them.