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Models, Logics, and Higher-Dimensional Categories: A Tribute to the Work of Mihály Makkai
 
Edited by: Bradd Hart McMaster University, Hamilton, ON, Canada
Thomas G. Kucera University of Manitoba, Winnipeg, MB, Canada
Anand Pillay University of Leeds, Leeds, United Kingdom and University of Illinois, Urbana, IL
Philip J. Scott University of Ottawa, Ottawa, ON, Canada
Robert A. G. Seely McGill University, Montreal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Front Cover for Models, Logics, and Higher-Dimensional Categories
Available Formats:
Softcover ISBN: 978-0-8218-7281-9
Product Code: CRMP/53
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
Electronic ISBN: 978-1-4704-1587-7
Product Code: CRMP/53.E
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $195.00
MAA Member Price: $175.50
AMS Member Price: $156.00
Front Cover for Models, Logics, and Higher-Dimensional Categories
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  • Front Cover for Models, Logics, and Higher-Dimensional Categories
  • Back Cover for Models, Logics, and Higher-Dimensional Categories
Models, Logics, and Higher-Dimensional Categories: A Tribute to the Work of Mihály Makkai
Edited by: Bradd Hart McMaster University, Hamilton, ON, Canada
Thomas G. Kucera University of Manitoba, Winnipeg, MB, Canada
Anand Pillay University of Leeds, Leeds, United Kingdom and University of Illinois, Urbana, IL
Philip J. Scott University of Ottawa, Ottawa, ON, Canada
Robert A. G. Seely McGill University, Montreal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques
Available Formats:
Softcover ISBN:  978-0-8218-7281-9
Product Code:  CRMP/53
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
Electronic ISBN:  978-1-4704-1587-7
Product Code:  CRMP/53.E
List Price: $130.00
MAA Member Price: $117.00
AMS Member Price: $104.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $195.00
MAA Member Price: $175.50
AMS Member Price: $156.00
  • Book Details
     
     
    CRM Proceedings & Lecture Notes
    Volume: 532011; 426 pp
    MSC: Primary 03; 18;

    This book deals with the main themes in Mihály Makkai's research career: traditional model theory, categorical model theory and logics, and higher-dimensional category theory. Included are both research papers and survey papers, giving useful material for experts and students in these fields. Particularly valuable are papers that show how the techniques and understanding in one field can be productively applied to another; examples are the paper by Harnik, which explains how Shelah's \(T^{eq}\) construction (in model theory) is the same as the categorical notion of pretopos completion; the paper by Kamensky, which gives category-theoretic treatments of sophisticated notions from stability theory; and the paper by Prest relating categorical logic and the model theory of modules. These and other papers in this volume should make this a valuable resource for any mathematician interested in classical or categorical model theory or higher dimensional category theory.

    Readership

    Graduate students and research mathematicians interested in model theory, logic, and higher-dimensional category theory.

  • Table of Contents
     
     
    • Chapters
    • The number of countable models in categories of sheaves
    • Pseudomonodacity and 2-stack completions
    • Purity and pure-injectivity for topological modules
    • Model theory vs. categorical logic: Two approaches to pretopos completion (a.k.a. $T^{\mathrm {eq}}$)
    • The dialectica monad and its cousins
    • A categorical approach to internality
    • Computable structures of Scott rank $\omega _1^{\mathrm {CK}}$
    • The Lorentz category in special relativity
    • A model-theoretic counterpart to Moishezon morphisms
    • Generic stability, regularity, and quasiminimality
    • Indexed Lawvere theories for local state
    • Model theory in additive categories
    • A derivation of Einstein’s vacuum field equations
    • An adventure into Hungarian word order with cyclic pregroups
    • No limit model in inaccessibles
    • The strict $\omega $-groupoid interpretation of type theory
    • Lax monoidal fibrations
  • Additional Material
     
     
  • Request Review Copy
Volume: 532011; 426 pp
MSC: Primary 03; 18;

This book deals with the main themes in Mihály Makkai's research career: traditional model theory, categorical model theory and logics, and higher-dimensional category theory. Included are both research papers and survey papers, giving useful material for experts and students in these fields. Particularly valuable are papers that show how the techniques and understanding in one field can be productively applied to another; examples are the paper by Harnik, which explains how Shelah's \(T^{eq}\) construction (in model theory) is the same as the categorical notion of pretopos completion; the paper by Kamensky, which gives category-theoretic treatments of sophisticated notions from stability theory; and the paper by Prest relating categorical logic and the model theory of modules. These and other papers in this volume should make this a valuable resource for any mathematician interested in classical or categorical model theory or higher dimensional category theory.

Readership

Graduate students and research mathematicians interested in model theory, logic, and higher-dimensional category theory.

  • Chapters
  • The number of countable models in categories of sheaves
  • Pseudomonodacity and 2-stack completions
  • Purity and pure-injectivity for topological modules
  • Model theory vs. categorical logic: Two approaches to pretopos completion (a.k.a. $T^{\mathrm {eq}}$)
  • The dialectica monad and its cousins
  • A categorical approach to internality
  • Computable structures of Scott rank $\omega _1^{\mathrm {CK}}$
  • The Lorentz category in special relativity
  • A model-theoretic counterpart to Moishezon morphisms
  • Generic stability, regularity, and quasiminimality
  • Indexed Lawvere theories for local state
  • Model theory in additive categories
  • A derivation of Einstein’s vacuum field equations
  • An adventure into Hungarian word order with cyclic pregroups
  • No limit model in inaccessibles
  • The strict $\omega $-groupoid interpretation of type theory
  • Lax monoidal fibrations
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