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

Martin Goldstern, Michael Pinsker, Saharon Shelah

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageEnglish
Pages (from-to)1115-1125
Number of pages11
JournalInternational Journal of Algebra and Computation
Volume23
Issue number5
DOIs
StatePublished - Aug 2013

Keywords

  • Borel set
  • Clone
  • closed set
  • complete analytic
  • ideal
  • upper density

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