A theorem about P(N)/fin

• Franklin Galindo Departamento de Lógica y Filosofı́a de la Ciencia, Universidad Central de Venezuela. Colaborardor Visitante del Departamento de Matemáticas, Instituto Venezolano de Investigaciones Cientı́ficas.

Keywords: linear order on P(N)/fin, partial order on P(N)/fin, Solovay’s model

Abstract

The objective of this article is to present an original proof of the following theorem: There is a generic extension of the Solovay's model $L (\mathbb{R})$ where there is a linear order of $P(\mathbb{N})/fin$ that extends to the partial order $(P(\mathbb{N})/fin),\leq^{\star})$. Linear orders of $P(\mathbb{N})/fin$ are important because, among other reasons, they allow constructing non-measurable sets.

References

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