Some very nice theorems on Almost-Disjoint Sets.
by Yiannis Souldatos
Abstract: Two sets A,B of the same cardinality, are almost disjoint if their intersection has cardinality less than the cardinality of A and B.
Given a set X how many almost disjoint subsets of X can we have of a given cardinality? The answer is very interesting, but partial, and involves both "absolute" theorems in ZFC, as well as forcing constructions.
Some background in set theory and forcing will be useful.
For More Information: Greg Hjorth: G.Hjorth@ms.unimelb.edu.au