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Book DetailsContemporary MathematicsVolume: 302; 2003; 285 ppMSC: 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.
ReadershipAdvanced graduate students and researchers interested in logic and foundations, algebra, and algebraic geometry.
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Table of Contents
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Articles
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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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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.
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 ]
