This volume outlines current developments in model theory and combinatorial set theory and presents state-of-the-art research. Well-known 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 long-standing 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 'pseudo-analytic' structures on algebraically closed fields. This result is part of his program of the model-theoretic 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.
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
Gewicht
ISBN-13
978-0-8218-2984-4 (9780821829844)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
(University of Michigan, Ann Arbor, USA)
Mad families and iteration theory by J. Brendle Nearly adequate sets by A. Blass How tall is the automorphism tower of a group? by J. D. Hamkins Reflection principles for the continuum by J. Stavi and J. Vaananen A theory of a generic function with derivations by B. Zilber Poly-regular ordered abelian groups by O. Belegradek On the logical strength of the automorphism groups of free nilpotent groups by V. Tolstykh Classification of the simple groups of finite Morley rank by T. Altinel Homogeneous model theory: Existence and categoricity by O. Lessmann Classification theory for abstract elementary classes by R. Grossberg Forking and multiplicity in first order theories by J. T. Baldwin Groups acting on geometries by T. Hyttinen Relative categoricity in linear orderings by W. Hodges Nonstandard analysis and an application to the symmetric group on natural numbers by M. Di Nasso and Y. Zhang On the ordering of the nonstandard real line by M. Di Nasso and M. Forti Order-types of models of Peano arithmetic by A. Bovykin and R. Kaye.
