Abstract:

Cardinal relations in the absence of the Axiom of Choice

After introducing the notion of a cardinal number (without
involving the Axiom of Choice), some basic results about 
their relation will be given (e.g., if M is an infinite set, then
the cardinality of the set of finite subsets of M is always
smaller than the cardinality of the power set of M). Then,
some rather counter-intuitive results will be discussed (like
the fact that there might be a partion of the real line which
has strictly more parts than real numbers exist) and a few
still open problems will be mentioned.
The talk is supposed to be quite elementary and the focus
will be on the results and the ideas of the proofs, and therefore
no specific knowledge of logic is required.