A problem about representations of countable, commutative semigroups leads to an analytic non-Borel set.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-1-2, author = {Robert Kaufman}, title = {Analytic sets in the theory of commutative semigroups}, journal = {Studia Mathematica}, volume = {231}, year = {2015}, pages = {3-6}, zbl = {1331.43004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-1-2} }
Robert Kaufman. Analytic sets in the theory of commutative semigroups. Studia Mathematica, Tome 231 (2015) pp. 3-6. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-1-2/