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Set Theory

Centre de Recerca Matemàtica Barcelona, 2003-2004

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  • © 2006

Overview

Editors:
  1. Joan Bagaria

    1. Departament de Lògica, Història I Filosofia de la Ciència, Universitat de Barcelona, Barcelona, Spain

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  2. Stevo Todorcevic

    1. Department of Mathematics, University of Toronto, Toronto, Canada
      C.N.R.S., UMR 7056, Université Paris 7, Paris Cedex 05, France

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  • Complements the lectures on Ramsey Methods in Analysis that appeared as separate book (ISBN 3-7643-7264-8)
  • Contributions by first-rate authors
  • Includes supplementary material: sn.pub/extras

Part of the book series: Trends in Mathematics (TM)

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-vii
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  2. Survey Papers

    1. An Ω-logic Primer

      • Joan Bagaria, Neus Castells, Paul Larson
      Pages 1-28

    2. Upper Semi-lattice Algebras and Combinatorics

      • M. Bekkali, D. Zhani
      Pages 29-54

    3. Small Definably-large Cardinals

      • Roger Bosch
      Pages 55-82

    4. Real-valued Measurable Cardinals and Well-orderings of the Reals

      • Andrés Eduardo Caicedo
      Pages 83-120

    5. Complexity of Sets and Binary Relations in Continuum Theory: A Survey

      • Alberto Marcone
      Pages 121-147

    6. Weak Systems of Gandy, Jensen and Devlin

      • A. R. D. Mathias
      Pages 149-224

    7. Some New Directions in Infinite-combinatorial Topology

      • Boaz Tsaban
      Pages 225-255

  3. Research Papers

    1. The Number of Near-Coherence Classes of Ultrafilters is Either Finite or \( 2^\mathfrak{c} \)

      • Taras Banakh, Andreas Blass
      Pages 257-273

    2. Stable Axioms of Set Theory

      • Sy-David Friedman
      Pages 275-283

    3. Forcing with Finite Conditions

      • Sy-David Friedman
      Pages 285-295

    4. Subgroups of Abelian Polish Groups

      • Greg Hjorth
      Pages 297-308

    5. On the Strength of Mutual Stationarity

      • Peter Koepke, Philip Welch
      Pages 309-320

    6. Part(κ, λ) and Part*(κ, λ)

      • Pierre Matet
      Pages 321-344

    7. Local Connectedness and Distance Functions

      • Charles Morgan
      Pages 345-400

    8. Bounded Martin’s Maximum and Strong Cardinals

      • Ralf Schindler
      Pages 401-406
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Keywords

About this book

This volume has its origins in the Research Programme on Set Theory and its Applications that took place at the Centre de Recerca Matemática (CRM) Barcelona from September 2003 to July 2004. It consists of two parts. The first contains survey papers on some of the mainstream areas of set theory, and the second contains original research papers.

The survey papers cover topics as Omega-logic, applications of set theory to lattice theory and Boolean algebras, real-valued measurable cardinals, complexity of sets and relations in continuum theory, weak subsystems of axiomatic set theory, definable versions of large cardinals, and selection theory for open covers of topological spaces. As for the research papers, they range from topics such as the number of near-coherence classes of ultrafilters, the consistency strength of bounded forcing axioms, P_\kappa\lambda combinatorics, some applications of morasses, subgroups of Abelian Polish groups, adding club subsets of \omega_2 with finite conditions, the consistency strength of mutual stationarity, and new axioms of set theory.

Editors and Affiliations

  • Departament de Lògica, Història I Filosofia de la Ciència, Universitat de Barcelona, Barcelona, Spain

    Joan Bagaria

  • Department of Mathematics, University of Toronto, Toronto, Canada

    Stevo Todorcevic

  • C.N.R.S., UMR 7056, Université Paris 7, Paris Cedex 05, France

    Stevo Todorcevic

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