The Non-existence of Extremal Objects of Set Theory and the Continuum Problem - Antipov, Mikhail Valentinovich (Journal of Informatics and Mathematical Sciences, 2011)
It is proved that the classical extremal objects of set theory are non-existent. It is also proved that the concepts of uncountability and continuum are erroneous and the first Hilbert problem is incorrect. The infinity axiom and all unlimited objects are unfounded as well.