Contemporary Mathematics 2003; 285 pp; softcover Volume: 302 ISBN10: 082182984X ISBN13: 9780821829844 List Price: US$84 Member Price: US$67.20 Order Code: CONM/302
 This volume outlines current developments in model theory and combinatorial set theory and presents stateoftheart research. Wellknown researchers report on their work in model theory and set theory with applications to algebra. The papers of J. Brendle and A. Blass present one of the most interesting areas of set theory. Brendle gives a very detailed and readable account of Shelah's solution for the longstanding problem of \(\mathrm{Con}(\mathfrak{d}<\mathfrak{a})\). It could be used in an advanced graduate seminar on set theory. Papers by T. Altinel, J. T. Baldwin, R. Grossberg, W. Hodges, T. Hyttinen, O. Lessmann, and B. Zilber deal with questions of model theory from the viewpoint of stability theory. Here, Zilber constructs an \(\omega\)stable complete theory of "pseudoanalytic" structures on algebraically closed fields. This result is part of his program of the modeltheoretic study of analytic structures by including Hrushovski's method in the analytic context. The book presents this and further developments in model theory. It is geared toward advanced graduate students and researchers interested in logic and foundations, algebra, and algebraic geometry. Readership Advanced graduate students and researchers interested in logic and foundations, algebra, and algebraic geometry. Table of Contents  J. Brendle  Mad families and iteration theory
 A. Blass  Nearly adequate sets
 J. D. Hamkins  How tall is the automorphism tower of a group?
 J. Stavi and J. Väänänen  Reflection principles for the continuum
 B. Zilber  A theory of a generic function with derivations
 O. Belegradek  Polyregular ordered abelian groups
 V. Tolstykh  On the logical strength of the automorphism groups of free nilpotent groups
 T. Altinel  Classification of the simple groups of finite Morley rank
 O. Lessmann  Homogeneous model theory: Existence and categoricity
 R. Grossberg  Classification theory for abstract elementary classes
 J. T. Baldwin  Forking and multiplicity in first order theories
 T. Hyttinen  Groups acting on geometries
 W. Hodges  Relative categoricity in linear orderings
 M. Di Nasso and Y. Zhang  Nonstandard analysis and an application to the symmetric group on natural numbers
 M. Di Nasso and M. Forti  On the ordering of the nonstandard real line
 A. Bovykin and R. Kaye  Ordertypes of models of Peano arithmetic
