# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Set-theoretic constructions of two-point sets

### Tom 203 / 2009

Fundamenta Mathematicae 203 (2009), 179-189 MSC: 03E35, 54G99. DOI: 10.4064/fm203-2-4

#### Streszczenie

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 $\hbox {ZFC}$, we demonstrate two new constructions of two-point sets. Our first construction shows that in $\hbox {ZFC}+ \hbox {CH}$ 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 $\hbox {ZF}$, we can show the existence of two-point sets without explicitly invoking the Axiom of Choice.

#### Autorzy

• Ben ChadSt Edmund Hall
Oxford, OX1 4AR, UK
e-mail
• Robin KnightWorcester College
Oxford OX1 2HB, UK
e-mail
• Rolf SuabedissenLady Margaret Hall
Oxford, OX2 6QA, UK
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek