| 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 |
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Book DetailsCRM Proceedings & Lecture NotesVolume: 53; 2011; 426 ppMSC: 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.
ReadershipGraduate students and research mathematicians interested in model theory, logic, and higher-dimensional category theory.
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Table of Contents
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Chapters
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The number of countable models in categories of sheaves
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Pseudomonodacity and 2-stack completions
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Purity and pure-injectivity for topological modules
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Model theory vs. categorical logic: Two approaches to pretopos completion (a.k.a. $T^{\mathrm {eq}}$)
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The dialectica monad and its cousins
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A categorical approach to internality
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Computable structures of Scott rank $\omega _1^{\mathrm {CK}}$
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The Lorentz category in special relativity
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A model-theoretic counterpart to Moishezon morphisms
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Generic stability, regularity, and quasiminimality
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Indexed Lawvere theories for local state
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Model theory in additive categories
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A derivation of Einstein’s vacuum field equations
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An adventure into Hungarian word order with cyclic pregroups
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No limit model in inaccessibles
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The strict $\omega $-groupoid interpretation of type theory
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Lax monoidal fibrations
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Additional Material
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- Book Details
- Table of Contents
- Additional Material
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- Request Review Copy
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.
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
