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A CLOSED ALGEBRA WITH A NON-BOREL CLONE AND AN IDEAL WITH A BOREL CLONE

    https://doi.org/10.1142/S0218196713500197Cited by:1 (Source: Crossref)

    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.

    AMSC: 08A40, 54H15, 22A30, 03E15

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