Transfinite inductions producing coanalytic sets

Zoltán Vidnyánszky¹

¹ Institute of Mathematics Eötvös Loránd University Pázmány Péter s. 1/c Budapest 1117, Hungary

Fundamenta Mathematicae, Tome 224 (2014) no. 2, pp. 155-174

Résumé

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 $C^1$ curve in a countable set.

Détail

DOI : 10.4064/fm224-2-2

Keywords: miller proved consistent existence coanalytic two point set hamel basis mad family these cases classical transfinite induction modified produce coanalytic set generalize his result formulating condition which easily applied situations reprove classical results application consistently there exists uncountable coanalytic subset plane intersects every curve countable set