More about recursive structures: descriptive complexity and zero-one laws

Abstract

This paper continues our work on infinite, recursive structures. We investigate the descriptive complexity of several logics over recursive structures, including first-order, second-order, and fixpoint logic, exhibiting connections between expressibility of a property and its computational complexity. We then address 0-1 laws, proposing a version that applies to recursive structures and using it to prove several non-expressibility results.