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Set-theoretic constructions of two-point sets

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Chad B., Knight R., Suabedissen R.

Fundamenta Mathematicae

2009

tom 203

nr 2

179-189

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.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Chad B.

1 Knight R.

1 Suabedissen R.

1 2009

Wyniki wyszukiwania

Set-theoretic constructions of two-point sets