A. Miller proved the consistent existence of a coanalytic two-point set, Hamel basis and MAD family. In these cases the classical transfinite induction can be modified to produce a coanalytic set. We generalize his result formulating a condition which can be easily applied in such situations. We reprove the classical results and as a new application we show that consistently there exists an uncountable coanalytic subset of the plane that intersects every C¹ curve in a countable set.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-2-2,
author = {Zolt\'an Vidny\'anszky},
title = {Transfinite inductions producing coanalytic sets},
journal = {Fundamenta Mathematicae},
volume = {227},
year = {2014},
pages = {155-174},
zbl = {1338.03093},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-2-2}
}
Zoltán Vidnyánszky. Transfinite inductions producing coanalytic sets. Fundamenta Mathematicae, Tome 227 (2014) pp. 155-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm224-2-2/