Set Theory and Logic

    

A Pathology of the Von Neumann Ordinals

Authors: David L. Selke

We show that the definition of the Von Neumann ordinal $omega_2$ fails to have the properties of an ordinal. In the notation that uses braces to denote ordinals, the ``depth" or ``height" of nesting of these braces becomes infinite leading to objects which have no top level of braces and which therefore have their elements undefined, leading to the conclusion that they are not sets at all, let alone ordinals. The least of these objects occurs before (that is, within) $omega_2$.

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[v1] 2024-10-21 04:32:35

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