February 20
Keshav Srinivasan,
Yeshiva University
Cohesive Powers of Algebraic Structures
One of the most important constructions is model theory is the ultrapower construction. We will discuss a computability-theoretic analogue of an ultrapower where non-principal ultrafilters, which are non-constructive, are replaced by cohesive sets. A cohesive set is a set that cannot be spit by any computably enumerable set. The resultant structure, known as the cohesive power, manages to be computable and constructive while maintaining analogues of the properties of ultrapowers. We will review recent results applying the cohesive power construction to algebraic extensions of Q.