Deciding the Continuum Hypothesis with the Inverse Powerset

Details Deciding the Continuum Hypothesis with the Inverse Powerset Deciding the Continuum Hypothesis with the Inverse Powerset

2010-11-03

arxiv.org/abs/1011.0787v2

Mathematics

Logic

36 pages; extended the previous version by 14 pages

Scientific paper

We introduce the concept of inverse powerset by adding three axioms to the Zermelo-Fraenkel set theory. This extends the Zermelo-Fraenkel set theory with a new type of set which is motivated by an intuitive meaning and interesting applications. We present different ways to extend the definition of cardinality and show that one implies the continuum hypothesis while another implies the negation of the continuum hypothesis. We will also explore the idea of empty sets of different cardinalities which could be seen as the empty counterpart of Cantor's theorem for infinite sets.

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