Theories of classification distinguish classes with
some good structure theorem from those for which
none is possible. Some classes (dense linear orders, for instance) are
non-classifiable in general, but are
classifiable when we consider only countable members. This paper
explores such a notion for classes of computable
structures by working out a sequence of examples.
¶
We follow recent work by Goncharov and Knight in using the degree of
the isomorphism problem for a class to
distinguish classifiable classes from non-classifiable. In this paper,
we calculate the degree of the isomorphism
problem for Abelian p-groups of bounded Ulm length. The result is a
sequence of classes whose isomorphism problems
are cofinal in the hyperarithmetical hierarchy. In the process, new
back-and-forth relations on such groups are
calculated.
@article{1107298523,
author = {Calvert, Wesley},
title = {The isomorphism problem for computable Abelian p-groups of bounded length},
journal = {J. Symbolic Logic},
volume = {70},
number = {1},
year = {2005},
pages = { 331-345},
language = {en},
url = {http://dml.mathdoc.fr/item/1107298523}
}
Calvert, Wesley. The isomorphism problem for computable Abelian p-groups of bounded length. J. Symbolic Logic, Tome 70 (2005) no. 1, pp. 331-345. http://gdmltest.u-ga.fr/item/1107298523/