Does Mathematics Need More Axioms?
Ahmet Çevik · 2021
In Chapter 17 we discuss about the debate on whether or not mathematics needs new axioms. The question is related to the problem of understanding the set-theoretical universe and of proving independent statements not known to be solvable within the current system of set theory. We discuss the attempt of set theorists in enlarging the constructible universe so as to obtain an ultimate expansion of the constructible hierarchy in which “all” known large cardinal axioms hold. We talk about the status of the Continuum Hypothesis, the inner model programme, and the hyperuniverse project.