Softcover ISBN:  9780821872819 
Product Code:  CRMP/53 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
Electronic ISBN:  9781470415877 
Product Code:  CRMP/53.E 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 

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 higherdimensional 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 categorytheoretic 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 higherdimensional category theory.

Table of Contents

Chapters

The number of countable models in categories of sheaves

Pseudomonodacity and 2stack completions

Purity and pureinjectivity 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 modeltheoretic 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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This book deals with the main themes in Mihály Makkai's research career: traditional model theory, categorical model theory and logics, and higherdimensional 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 categorytheoretic 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 higherdimensional category theory.

Chapters

The number of countable models in categories of sheaves

Pseudomonodacity and 2stack completions

Purity and pureinjectivity 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 modeltheoretic 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