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arXiv · 1112.0774

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

Martin Goldstern·Michael Pinsker·Saharon Shelah
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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.

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Martin Goldstern, Michael Pinsker, Saharon Shelah. 2011-12-04. A closed algebra with a non-Borel clone and an ideal with a Borel clone. https://arxiv.org/abs/1112.0774

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