This year 2013 marks the centenary of Professor Andrzej Mostowski (1913–1975), one of the leading logicians of the 20th century. A student and collaborator of both Kurt Gödel and Alfred Tarski, Mostowski contributed significantly to all areas of Foundations of Mathematics, with the most spectacular achievements in Set Theory, Model Theory, Abstract Model Theory, Recursion Theory, and investigations of the Incompleteness phenomena in Mathematics.

Professor Mostowski built a significant center of foundational investigations in Warsaw, Poland, after WWII. In the realities of an ideologically divided European continent, he was able to create a unique enclave where the logicians of the East and the West met, communicated, and collaborated towards the common goal of furthering foundational research.

The passage of time did not bury his work; a number of techniques taught in the courses of Logic, Set Theory and, more generally, Foundations of Mathematics carry his name, recognizing his contributions. These include: the Fraenkel-Mostowski permutation models technique for independence proofs in Set Theory, the Mostowski Contraction Lemma, the Ehrenfeucht-Mostowski models with indiscernibles, Mostowski's generalized quantifiers, the Kleene-Mostowski descriptive hierarchy of sets, and many other, more specialized results.

The centenaries of Kurt Gödel, Alfred Tarski and Alan Turing were celebrated during the past decade. To commemorate and honor the centenary of Andrzej Mostowski, and reflect on his contributions and on the past and future of Foundations of Mathematics, logicians of many countries will meet in Warsaw, Poland, in October 2013. Here we would like to express our sincere thanks to all those individuals and organizations involved in organizing, cosponsoring, or contributing to this meeting.

The editors of the present volume, as well as the publisher, all directly owing their education and first steps in foundational research to Professor Mostowski, hope that this first reprint of the volume forms a well-deserved tribute commemorating his manifold contributions to Logic and Foundations and will engage researchers and students in a consideration about the current state-of-the-art and the importance of problems and directions pioneered by Mostowski. The work in Mostowski's tradition continues. We hope that this volume will remind the reader of the person and work of a great mathematician of the 20th century.

A. Ehrenfeucht, E.H. Fredriksson, V.W. Marek and M. Srebrny

June 2013