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.
Maximal computably enumerable sets and vector spaces
18.12.2014 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25