Combinatorial theory is largely the study of properties that a set or family of sets may have by virtue of its cardinality, although this may be widened to consider related properties held by sets carrying a simple structure, such as ordered or well ordered sets. These properties are relevant to either finite or infinite sets, although frequently the questions that pose interesting problems for finite sets are either meaningless or trivial for infinite sets, and vice-versa. There has been a recent great upsurge in the study of finite combinatorial problems, and a significant, though more manageable, increase in interest in the combinatorial properties of infinite sets. This book deals solely with combinatorial questions pertinent to infinite sets.

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