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On Russell and anti Russell-cardinals

Horst Herrlich, Kyriakos Keremedis, Eleftherios Tachtsis

Abstract


In the absence of the Axiom of Choice we study countable families of 2-element sets with no choice functions which either have infinite subfamilies with a choice function or no infinite subfamilies with a choice function.

Keywords: Axiom of Choice; Russell-cardinals; anti Russell-cardinals; prime cardinals; amorphous cardinals; permutation models.

Quaestiones Mathematicae 33(2010), 1–9

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Quaestiones Mathematicae.   ISSN: 1607-3606