Kurt Gödel Research Center

2014 seminar talk: Maximal computably enumerable sets and vector spaces

Talk held by Valentina Harizanov (The George Washington University, Washington, D.C., USA) at the KGRC seminar on 2014-12-18.

Abstract

A computably enumerable set is maximal if its complement is infinite but cannot be split by any computably enumerable set into two infinite parts. Maximal sets play an important role in computability theory, especially in the study of the lattice of computably enumerable sets. They are co-atoms in its quotient lattice modulo finite sets. Similarly, maximal vector spaces play an important role in the study of the lattice of computably enumerable vector spaces and its quotient lattice modulo finite dimension. We investigate principal filters determined by maximal spaces and how algebraic structure interacts with computability theoretic properties.