The size of real numbers and other mysteries of the continuum function

In Hilbert’s famous list of problems for mathematicians in the 20th century, the first one was to resolve the Continuum Hypothesis, namely to determine the exact size of the set of real numbers. The answer was unexpected as it turned out that it cannot be determined from the standard axioms we use in mathematics. The Continuum Hypothesis is only the first step in understanding the complexity of the continuum function, the function that gives the cardinality of power sets of infinite sets.

The slides are in greek.