**Contemporary Mathematics**

Volume: 302;
2003;
285 pp;
Softcover

MSC: Primary 03; 20;

Print ISBN: 978-0-8218-2984-4

Product Code: CONM/302

List Price: $84.00

Individual Member Price: $67.20

**Electronic ISBN: 978-0-8218-7892-7
Product Code: CONM/302.E**

List Price: $84.00

Individual Member Price: $67.20

# Logic and Algebra

Share this page *Edited by *
*Yi Zhang*

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.

#### Table of Contents

# Table of Contents

## Logic and Algebra

- Contents v6 free
- Mad families and iteration theory 110 free
- Nearly adequate sets 3342
- How tall is the automorphism tower of a group? 4958
- Reflection principles for the continuum 5968
- A theory of a generic function with derivations 8594
- Poly-regular ordered Abelian groups 101110
- On the logical strength of the automorphism groups of free nilpotent groups 113122
- Classification of the simple groups of finite Morley rank 121130
- Homogeneous model theory: existence and categoricity 149158
- Classification theory for abstract elementary classes 165174
- Forking and multiplicity in first order theories 205214
- Groups acting on geometries 221230
- Relative categoricity in linear orderings 235244
- Nonstandard analysis and an application to the symmetric group on natural numbers 249258
- On the ordering of the nonstandard real line 259268
- Order-types of models of Peano arithmetic 275284

#### Readership

Advanced graduate students and researchers interested in logic and foundations, algebra, and algebraic geometry.