This book, *Consequences of the Axiom of Choice*, is
a comprehensive listing of statements that have been proved in the
last 100 years using the axiom of choice. Each consequence, also
referred to as a form of the axiom of choice, is assigned a
number.

Part I is a listing of the forms by number. In this
part each form is given together with a listing of all statements
known to be equivalent to it (equivalent in set theory without the
axiom of choice). In Part II the forms are arranged by topic. In
Part III we describe the models of set theory which are used to show
non-implications between forms. Part IV, the notes section, contains
definitions, summaries of important sub-areas and proofs that are not
readily available elsewhere. Part V gives references for the
relationships between forms and Part VI is the bibliography.

Part VII is contained on the floppy disk which is enclosed in the
book. It contains a table with form numbers as row and column
headings. The entry in the table in row $n$, column $k$ gives the status
of the implication “form $n$ implies form $k$”. Software for
easily extracting information from the table is also provided.

**Features:**

complete summary of all the work done in the last 100 years on
statements that are weaker than the axiom of choice

software provided gives complete, convenient access to information
about relationships between the various consequences of the axiom of
choice and about the models of set theory

descriptions of more than 100 models used in the study of the axiom
of choice

an extensive bibliography

** About the software:** Tables 1 and 2 are accessible on the
PC-compatible software included with the book. In addition, the
program maketex.c in the software package will create tex files
containing copies of Table 1 and Table 2 which may then be printed.
(Tables 1 and 2 are also available at the authors' Web sites:
http://www.math.purdue.edu/$\sim$jer/ or
http://www.emunix.emich.edu/$\sim$phoward/.) Detailed instructions for
setting up and using the software are included in the book's
Introduction, and technical support is available directly from the authors.

Readership

Mathematicians with a primary interest in set theory
and who do research on the axiom of choice; philosophers interested in
the role of the axiom of choice in the foundations of
mathematics.