basic constructions: strong axioms further Cantor’s continuum problem is simply the question: How many points are there on a straight line in Euclidean space? In other terms, the question is: How many different sets of integers do there exist? [Gödel 1947 p 515] The continuum hypothesis is a famous problem of set theory concerning the cardinality of the Dedekind real numbers (the “continuum”). The hypothesis in its classical form goes back to G. Cantor and was on top of Hilbert's list of open...