This proposal is designed to promote multi-disciplinary training and research in model theory, a branch of mathematical logic dealing abstractly with structures. In the past decade, model theory has reached a new maturity, allowing for a strengthening o f existing connections with, and striking applications to, other areas of mathematics. A network is the ideal setting for providing the adequate training needed to preserve and nourish this impetus. The proposed network involves most European model the orists (including all leading experts), as well as a few scientists from the related branches of mathematics. A feature of European model theory is the dispersion of its scientists, so that collaboration between the various research centers is essentia l. Besides pure model theory, whose development is crucial for applications, two of the main themes of research of the proposed network are: fields with added structure (orderings, operators, and valuations) and groups.
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