# Mathematical Applications of Category Theory

Share this page *Edited by *
*John W. Gray*

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.

# Table of Contents

## Mathematical Applications of Category Theory

- Table of Contents vii8 free
- Introduction 110 free
- The Interaction Between Category Theory and Set Theory 514
- Synthetic Calculus of Variations 3039
- The Representation of Limits, Lax Limits and Homotopy Limits as Sections 6372
- Open Locales and Exponentiation 8493
- Eilenberg-Mac Lane Toposes and Cohomology 117126
- A Combinatorial Theory of Connections 132141
- Aspects of Higher Order Categorical Logic 145154
- A Stone-Type Representation Theory for First Order Logic 175184
- Topological Universes and Smooth Gelfand-Naimark Duality 244253
- Applications of the Dual Functor in Banach Spaces 277286