A closed algebra with a non-Borel clone and an ideal with a Borel clone

Details A closed algebra with a non-Borel clone and an ideal with a Borel clone A closed algebra with a non-Borel clone and an ideal with a Borel clone

2011-12-04

arxiv.org/abs/1112.0774v1

Mathematics

Rings and Algebras

9 pages

Scientific paper

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.

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