Finite and Infinite Combinatorics in Sets and Logic

the long version

This book highlights the newly emerging connections between problems in finite combinatorics and graph theory on the one hand and the more foundational subjects of logic and set theory on the other.<br/> One of the more obvious routes for such a connection is the straightforward generalization of certain definitions and problems from the finite to the infinite, and sometimes the other way around. Another one is to generalize some definitions and find the appropriate new concepts for the new setting, for example the discussion of ends of graphs.<br/> The realization of the importance of homogeneous structures and their connection with logic, as well as with finite structure theory, is a good example of the connection between finite and infinite structures. Almost all of the articles in the present book touch in one way or another on homogeneous structures. The discussion of the 0--1 law, of Ramsey theory for finite and infinite structures, and of divisibility theory highlight this.<br/>