Original Articles

An Independence Result Concerning Russell-Cardinals

Published in: Quaestiones Mathematicae
Volume 31 , issue 2 , 2008 , pages: 173–177

DOI: 10.2989/QM.2008.31.2.6.478

Author(s): Eleftherios Tachtsis

Keywords: AXIOM OF CHOICE , RUSSELL-CARDINALS , DEDEKIND-FINITE SETS , DEDEKIND-CARDINALS

Abstract

We show that it is consistent with ZF ⁰ that there exists a Russell-cardinal α such that the cardinals α ² and 2^α are incomparable. This answers in the negative a related question from Herrlich and Tachtsis “On the number of Russell's socks or 2 + 2 + 2 +... =?”.

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