Computability Seminar MSRI program on DDC- Generically computable structures

Organizer: V. Harizanov

For link contact [email protected]

Friday, October 2, 12:00-1:00 on Zoom

Speaker:  Doug Cenzer, University of Florida

Title: Generically computable structures

Abstract:  We define notions of generically and coarsely computable and computably enumerable structures.  There are two directions in which these notions could potentially trivialize: either all structures could have a densely computable copy or only those having a computable (or computably enumerable) copy.  We show that particular classes of structures realize each of these extremal conditions, while other classes realize neither of them. To further explore these concepts, we introduce a graded family of elementarity conditions for substructures, in which we require that the dense sets under consideration be a strong substructure of the original structure.