Category theory has had important uses in logic since the invention of topos theory in the early 1960s, and logic has always been an important component of theoretical computer science. A new development has been the increase in direct interactions between category theory and computer science. In June 1987, an AMS-IMS-SIAM Summer Research Conference on Categories in Computer Science and Logic was held at the University of Colorado in Boulder. The aim of the conference was to bring together researchers working on the interconnections between category theory and computer science or between computer science and logic. The conference emphasized the ways in which the general machinery developed in category theory could be applied to specific questions and be used for category-theoretic studies of concrete problems. This volume represents the proceedings of the conference. (Some of the participants' contributions have been published elsewhere.) The papers published here relate to three different aspects of the conference. The first concerns topics relevant to all three fields, including, for example, Horn logic, lambda calculus, normal form reductions, algebraic theories, and categorical models for computability theory. In the area of logic, topics include semantical approaches to proof-theoretical questions, internal properties of specific objects in (pre-) topoi and their representations, and categorical sharpening of model-theoretic notions. Finally, in the area of computer science, the use of category theory in formalizing aspects of computer programming and program design is discussed.
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.
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