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Logic and Algebra
Edited by: Yi Zhang, University of Michigan, Ann Arbor, MI
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Contemporary Mathematics
2003; 285 pp; softcover
Volume: 302
ISBN-10: 0-8218-2984-X
ISBN-13: 978-0-8218-2984-4
List Price: US$80
Member Price: US$64
Order Code: CONM/302
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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.

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 -- Poly-regular 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 -- Order-types of models of Peano arithmetic
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