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.
Original language | English |
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Pages (from-to) | 1115-1125 |
Number of pages | 11 |
Journal | International Journal of Algebra and Computation |
Volume | 23 |
Issue number | 5 |
DOIs | |
State | Published - Aug 2013 |
Keywords
- Borel set
- Clone
- closed set
- complete analytic
- ideal
- upper density