Transfinite inductions producing coanalytic sets

@article{ZoltánVidnyánszky2014,
abstract = {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.},
author = {Zoltán Vidnyánszky},
journal = {Fundamenta Mathematicae},
keywords = {coanalytic set; constructibility; Hamel basis; two-point set; transfinite induction},
language = {eng},
number = {2},
pages = {155-174},
title = {Transfinite inductions producing coanalytic sets},
url = {http://eudml.org/doc/282749},
volume = {224},
year = {2014},
}

TY - JOUR
AU - Zoltán Vidnyánszky
TI - Transfinite inductions producing coanalytic sets
JO - Fundamenta Mathematicae
PY - 2014
VL - 224
IS - 2
SP - 155
EP - 174
AB - 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.
LA - eng
KW - coanalytic set; constructibility; Hamel basis; two-point set; transfinite induction
UR - http://eudml.org/doc/282749
ER -