Mathematicians interested in understanding the directions of current
research in set theory will not want to overlook this book, which contains the
proceedings of the AMS Summer Research Conference on Axiomatic Set Theory,
held in Boulder, Colorado, June 19–25, 1983. This was the first large
meeting devoted exclusively to set theory since the legendary 1967 UCLA
meeting, and a large majority of the most active research mathematicians in
the field participated. All areas of set theory, including constructibility,
forcing, combinatorics and descriptive set theory, were represented; many of
the papers in the proceedings explore connections between areas. Readers
should have a background of graduate-level set theory.

There is a paper by **S.~Shelah** applying proper forcing to obtain
consistency results on combinatorial cardinal “invariants” below
the continuum, and papers by **R.~David** and **S.~Freidman** on
properties of $0^\#$. Papers by **A.~Blass**,
**H.-D.~Donder**, **T.~Jech** and **W.~Mitchell** involve inner
models with measurable cardinals and various combinatorial properties.
**T.~Carlson** largely solves the pin-up problem, and **D.~Velleman**
presents a novel construction of a Souslin tree from a morass.
**S.~Todorcevic** obtains the strong failure of the \qedprinciple from
the Proper Forcing Axiom and **A.~Miller** discusses properties of a new
species of perfect-set forcing. **H.~Becker** and **A.~Kechris**
attack the third Victoria Delfino problem while **W.~Zwicker** looks at
combinatorics on $P_\kappa(\lambda)$ and **J.~Henle** studies
infinite-exponent partition relations. **A.~Blass** shows that if every
vector space has a basis then $AC$ holds. **I.~Anellis** treats
the history of set theory, and **W.~Fleissner** presents set-theoretical
axioms of use in general topology.