Construction of a Well-Ordering on the Continuum: Consequences for the Continuum Hypothesis
The subject of the book is characterized in the preface as an attempt, which “is perhaps a very particular point of the mathematical sciences, but it is simple and uses no elaborated notion”. The author presents a proof of the continuum hypothesis (CH) from set theory. The framework is not usual Zermelo-Fraenkel set theory (ZFC). As informally indicated, a “missing” axiom is added to ZFC, which makes it possible to present a proof of CH. The author discusses particular “missing” axioms of set theory (e.g., the axiom of projective determinancy) and he adds various comments on the obtained results.