Set-theoretic constructions of two-point sets

Ben Chad, Robin Knight, and Rolf Suabedissen. "Set-theoretic constructions of two-point sets." Fundamenta Mathematicae 203.2 (2009): 179-189. <http://eudml.org/doc/283121>.

@article{BenChad2009,
abstract = {A two-point set is a subset of the plane which meets every line in exactly two points. By working in models of set theory other than ZFC, we demonstrate two new constructions of two-point sets. Our first construction shows that in ZFC + CH there exist two-point sets which are contained within the union of a countable collection of concentric circles. Our second construction shows that in certain models of ZF, we can show the existence of two-point sets without explicitly invoking the Axiom of Choice.},
author = {Ben Chad, Robin Knight, Rolf Suabedissen},
journal = {Fundamenta Mathematicae},
keywords = {two-point set; continuum hypothesis; axiom of choice},
language = {eng},
number = {2},
pages = {179-189},
title = {Set-theoretic constructions of two-point sets},
url = {http://eudml.org/doc/283121},
volume = {203},
year = {2009},
}

TY - JOUR
AU - Ben Chad
AU - Robin Knight
AU - Rolf Suabedissen
TI - Set-theoretic constructions of two-point sets
JO - Fundamenta Mathematicae
PY - 2009
VL - 203
IS - 2
SP - 179
EP - 189
AB - A two-point set is a subset of the plane which meets every line in exactly two points. By working in models of set theory other than ZFC, we demonstrate two new constructions of two-point sets. Our first construction shows that in ZFC + CH there exist two-point sets which are contained within the union of a countable collection of concentric circles. Our second construction shows that in certain models of ZF, we can show the existence of two-point sets without explicitly invoking the Axiom of Choice.
LA - eng
KW - two-point set; continuum hypothesis; axiom of choice
UR - http://eudml.org/doc/283121
ER -