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Logic and Algebra
 
Edited by: Yi Zhang University of Michigan, Ann Arbor, MI
Front Cover for Logic and Algebra
Available Formats:
Softcover ISBN: 978-0-8218-2984-4
Product Code: CONM/302
List Price: $90.00
MAA Member Price: $81.00
AMS Member Price: $72.00
Electronic ISBN: 978-0-8218-7892-7
Product Code: CONM/302.E
List Price: $84.00
MAA Member Price: $75.60
AMS Member Price: $67.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Front Cover for Logic and Algebra
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  • Front Cover for Logic and Algebra
  • Back Cover for Logic and Algebra
Logic and Algebra
Edited by: Yi Zhang University of Michigan, Ann Arbor, MI
Available Formats:
Softcover ISBN:  978-0-8218-2984-4
Product Code:  CONM/302
List Price: $90.00
MAA Member Price: $81.00
AMS Member Price: $72.00
Electronic ISBN:  978-0-8218-7892-7
Product Code:  CONM/302.E
List Price: $84.00
MAA Member Price: $75.60
AMS Member Price: $67.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 3022003; 285 pp
    MSC: Primary 03; 20;

    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
     
     
    • Articles
    • Jörg Brendle - Mad families and iteration theory [ MR 1928381 ]
    • Andreas Blass - Nearly adequate sets [ MR 1928382 ]
    • Joel David Hamkins - How tall is the automorphism tower of a group? [ MR 1928383 ]
    • Jonathan Stavi and Jouko Väänänen - Reflection principles for the continuum [ MR 1928384 ]
    • Boris Zilber - A theory of a generic function with derivations [ MR 1928385 ]
    • Oleg Belegradek - Poly-regular ordered abelian groups [ MR 1928386 ]
    • Vladimir Tolstykh - On the logical strength of the automorphism groups of free nilpotent groups [ MR 1928387 ]
    • Tuna Altınel - Classification of the simple groups of finite Morley rank [ MR 1928388 ]
    • Olivier Lessmann - Homogeneous model theory: existence and categoricity [ MR 1928389 ]
    • Rami Grossberg - Classification theory for abstract elementary classes [ MR 1928390 ]
    • John T. Baldwin - Forking and multiplicity in first order theories [ MR 1928391 ]
    • Tapani Hyttinen - Groups acting on geometries [ MR 1928392 ]
    • Wilfrid Hodges - Relative categoricity in linear orderings [ MR 1928393 ]
    • Mauro Di Nasso and Yi Zhang - Nonstandard analysis and an application to the symmetric group on natural numbers [ MR 1928394 ]
    • Mauro Di Nasso and Marco Forti - On the ordering of the nonstandard real line [ MR 1928395 ]
    • Andrey Bovykin and Richard Kaye - Order-types of models of Peano arithmetic [ MR 1928396 ]
  • Request Review Copy
  • Get Permissions
Volume: 3022003; 285 pp
MSC: Primary 03; 20;

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.

  • Articles
  • Jörg Brendle - Mad families and iteration theory [ MR 1928381 ]
  • Andreas Blass - Nearly adequate sets [ MR 1928382 ]
  • Joel David Hamkins - How tall is the automorphism tower of a group? [ MR 1928383 ]
  • Jonathan Stavi and Jouko Väänänen - Reflection principles for the continuum [ MR 1928384 ]
  • Boris Zilber - A theory of a generic function with derivations [ MR 1928385 ]
  • Oleg Belegradek - Poly-regular ordered abelian groups [ MR 1928386 ]
  • Vladimir Tolstykh - On the logical strength of the automorphism groups of free nilpotent groups [ MR 1928387 ]
  • Tuna Altınel - Classification of the simple groups of finite Morley rank [ MR 1928388 ]
  • Olivier Lessmann - Homogeneous model theory: existence and categoricity [ MR 1928389 ]
  • Rami Grossberg - Classification theory for abstract elementary classes [ MR 1928390 ]
  • John T. Baldwin - Forking and multiplicity in first order theories [ MR 1928391 ]
  • Tapani Hyttinen - Groups acting on geometries [ MR 1928392 ]
  • Wilfrid Hodges - Relative categoricity in linear orderings [ MR 1928393 ]
  • Mauro Di Nasso and Yi Zhang - Nonstandard analysis and an application to the symmetric group on natural numbers [ MR 1928394 ]
  • Mauro Di Nasso and Marco Forti - On the ordering of the nonstandard real line [ MR 1928395 ]
  • Andrey Bovykin and Richard Kaye - Order-types of models of Peano arithmetic [ MR 1928396 ]
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