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 This volume also contains the unpublished but significant thesis of Hamid Lesan (1951-2006) as well as other original papers on topics addressed in Woods’s thesis and life’s work that were first presented at the 31st Journées sur les Arithmétiques Faibles meeting held in Samos, Greece, in 2012.

Patrick Cégielski is professor in the Département Informatique at Université Paris-Est Créteil. Charalampos Cornaros is assistant professor of mathematics at the University of the Aegean, Greece. Costas Dimitracopoulos is professor in the Faculty of Philosophy and History of Science at the National and Kapodistrian University of Athens, Greece.