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Mathematical Applications of Category Theory
Edited by: John W. Gray
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Contemporary Mathematics
1984; 307 pp; softcover
Volume: 30
Reprint/Revision History:
reprinted 1991
ISBN-10: 0-8218-5032-6
ISBN-13: 978-0-8218-5032-9
List Price: US$48
Member Price: US$38.40
Order Code: CONM/30
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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

  • A. Blass -- The interaction between category theory and set theory
  • M. Bunge and M. Heggie -- Synthetic calculus of variations
  • J. W. Gray -- The representation of limits, lax limits and homotopy limits as sections
  • P. T. Johnstone -- Open locales and exponentiation
  • A. Joyal and G. Wraith -- Eilenberg-Mac Lane toposes and cohomology
  • A. Kock -- A combinatorial theory of connections
  • J. Lambek and P. J. Scott -- Aspects of higher order categorical logic
  • M. Makkai -- A Stone-type representation theory for first order logic
  • L. D. Nel -- Topological universes and smooth Gelfand-Naimark duality
  • J. W. Pelletier -- Applications of the dual functor in Banach spaces
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