Computable Homogeneous Boolean Algebras
Pavel Alaev (alaev@math.nsc.ru)
Novosibirsk State University (Russia)
We propose a criterion saying when a homogeneous Boolean algebra has
a computable copy. Andrei Morozov proved that such an
algebra can be described by an invariant which is a subset of
the set of natural numbers.
We introduce a hierarchy of D0w -sets which generalizes
Feiner's hierarchy. A countable homogeneous Boolean algebra has a
computable copy if and only if its invariant belongs to a class
of this hierarchy.
A way to pass from a hyperarithmetical quotient Boolean algebra to
a computable Boolean algebra is also considered.