Set-theoretic constructions of two-point sets

• Autorzy: Ben Chad , Robin Knight , Rolf Suabedissen
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54G99: None of the above, but in this section
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2009
• Tom: 203
• Numer: 2
• Strony: 179-189

Daty

wydano

2009

Twórcy

autor

Ben Chad

• St Edmund Hall, Oxford, OX1 4AR, UK

autor

Robin Knight

• Worcester College, Oxford OX1 2HB, UK

autor

Rolf Suabedissen

• Lady Margaret Hall, Oxford, OX2 6QA, UK

Identyfikatory

DOI

10.4064/fm203-2-4