A closed algebra with a non-Borel clone and an ideal with a Borel clone
Rings and Algebras
2011-12-06 v1 Logic
Abstract
Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is not Borel. Moreover, we provide an example of a coatom in the clone lattice whose obvious definition via an ideal of subsets of natural numbers would suggest that it is complete coanalytic, but which turns out to be a rather simple Borel set.
Cite
@article{arxiv.1112.0774,
title = {A closed algebra with a non-Borel clone and an ideal with a Borel clone},
author = {Martin Goldstern and Michael Pinsker and Saharon Shelah},
journal= {arXiv preprint arXiv:1112.0774},
year = {2011}
}
Comments
9 pages