The Annual European Meeting of the Association for Symbolic Logic, generally known as the Logic Colloquium, is the most prestigious annual meeting in the field. Many of the papers presented there are invited surveys of developments, and the rest of the papers are chosen to complement the invited talks. This 2007 volume includes surveys, tutorials, and selected research papers from the 2005 meeting. Highlights include three papers on different aspects of connections between model theory and algebra; a survey of major advances in combinatorial set theory; a tutorial on proof theory and modal logic; and a description of Bernay's philosophy of mathematics.

The field of weak arithmetics is an application of logical methods to number theory that was developed by mathematicians, philosophers, and theoretical computer scientists. New Studies in Weak Arithmetics is dedicated to late Australian mathematician Alan Robert Woods (1953-2011), whose seminal thesis is published here for the first time. This volume also contains the unpublished but significant thesis of Hamid Lesan (1951-2006) as well as other original papers on topics addressed in Woods' thesis and life's work that were first presented at the 31st Journees sur les Arithmetiques Faibles meeting held in Samos, Greece, in 2012.