Speaker
Dariusz Kalociński
Institute of Computer Science, Polish Academy of Sciences
Talks at this conference:
Friday, 17:45, J222 
Scott ranks and intended models 
Certain mathematical theories are about a single, socalled intended, structure (e.g., arithmetic is about natural numbers) while others investigate general properties of all structures they axiomatize (e.g., group theory). The former theories are known as nonalgebraic, while the latter as algebraic. One of the problems in the philosophy of mathematics concerns a systematic explanation of this phenomenon, ideally providing a theoretical notion that could explicate the concept of intendedness. I will briefly review some of the existing philosophical approaches regarding arithmetic, including the work of Halbach and Horsten [1], Button and Smith [2] and Walter Dean [3], among others. In the main part of my talk I will suggest a novel perspective on this problem, based on the measures of complexity of models, such as Scott ranks. I will try to explain basic technicalities involved in this notion and illustrate how it deals with the problem at hand with a few examples of algebraic as well as nonalgebraic theories, including PA (by leveraging results from [4]) and weaker systems like Robinson’s or Presburger’s arithmetic. Bibliography
