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Abstract: In infinitary combinatorics it is often natural to generalize problems from finite combinatorics to the space of natural numbers, a countable set. We will go up another step and look at combinatorics on the real line. A combinatorial characteristic of the continuum is an uncountable cardinal between the first uncountable cardinal the continuum that describes a combinatorial or analytical property of the continuum. In contexts where the continuum hypothesis fails, these characteristics give a means of understanding the structure of “small” uncountable cardinalities.
I will also give a brief primer on any necessary set-theoretic preliminaries (of which there are few).