First Order Categorical Logic

First Order Categorical Logic
Author :
Publisher : Springer
Total Pages : 317
Release :
ISBN-10 : 9783540371007
ISBN-13 : 3540371001
Rating : 4/5 (07 Downloads)

Book Synopsis First Order Categorical Logic by : M. Makkai

Download or read book First Order Categorical Logic written by M. Makkai and published by Springer. This book was released on 2006-11-15 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Higher-Order Categorical Logic

Introduction to Higher-Order Categorical Logic
Author :
Publisher : Cambridge University Press
Total Pages : 308
Release :
ISBN-10 : 0521356539
ISBN-13 : 9780521356534
Rating : 4/5 (39 Downloads)

Book Synopsis Introduction to Higher-Order Categorical Logic by : J. Lambek

Download or read book Introduction to Higher-Order Categorical Logic written by J. Lambek and published by Cambridge University Press. This book was released on 1988-03-25 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.

Categorical Logic and Type Theory

Categorical Logic and Type Theory
Author :
Publisher : Gulf Professional Publishing
Total Pages : 784
Release :
ISBN-10 : 0444508538
ISBN-13 : 9780444508539
Rating : 4/5 (38 Downloads)

Book Synopsis Categorical Logic and Type Theory by : B. Jacobs

Download or read book Categorical Logic and Type Theory written by B. Jacobs and published by Gulf Professional Publishing. This book was released on 2001-05-10 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.

Topoi

Topoi
Author :
Publisher : Elsevier
Total Pages : 569
Release :
ISBN-10 : 9781483299211
ISBN-13 : 148329921X
Rating : 4/5 (11 Downloads)

Book Synopsis Topoi by : R. Goldblatt

Download or read book Topoi written by R. Goldblatt and published by Elsevier. This book was released on 2014-06-28 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.

Uncountably Categorical Theories

Uncountably Categorical Theories
Author :
Publisher : American Mathematical Soc.
Total Pages : 132
Release :
ISBN-10 : 0821897454
ISBN-13 : 9780821897454
Rating : 4/5 (54 Downloads)

Book Synopsis Uncountably Categorical Theories by : Boris Zilber

Download or read book Uncountably Categorical Theories written by Boris Zilber and published by American Mathematical Soc.. This book was released on with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.

Sketches of an Elephant: A Topos Theory Compendium

Sketches of an Elephant: A Topos Theory Compendium
Author :
Publisher : Oxford University Press
Total Pages : 836
Release :
ISBN-10 : 0198515987
ISBN-13 : 9780198515982
Rating : 4/5 (87 Downloads)

Book Synopsis Sketches of an Elephant: A Topos Theory Compendium by : P. T. Johnstone

Download or read book Sketches of an Elephant: A Topos Theory Compendium written by P. T. Johnstone and published by Oxford University Press. This book was released on 2002-09-12 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topos Theory is a subject that stands at the junction of geometry, mathematical logic and theoretical computer science, and it derives much of its power from the interplay of ideas drawn from these different areas. Because of this, an account of topos theory which approaches the subject from one particular direction can only hope to give a partial picture; the aim of this compendium is to present as comprehensive an account as possible of all the main approaches and to thereby demonstrate the overall unity of the subject. The material is organized in such a way that readers interested in following a particular line of approach may do so by starting at an appropriate point in the text.

Basic Category Theory for Computer Scientists

Basic Category Theory for Computer Scientists
Author :
Publisher : MIT Press
Total Pages : 117
Release :
ISBN-10 : 9780262326452
ISBN-13 : 0262326450
Rating : 4/5 (52 Downloads)

Book Synopsis Basic Category Theory for Computer Scientists by : Benjamin C. Pierce

Download or read book Basic Category Theory for Computer Scientists written by Benjamin C. Pierce and published by MIT Press. This book was released on 1991-08-07 with total page 117 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Category theory is a branch of pure mathematics that is becoming an increasingly important tool in theoretical computer science, especially in programming language semantics, domain theory, and concurrency, where it is already a standard language of discourse. Assuming a minimum of mathematical preparation, Basic Category Theory for Computer Scientists provides a straightforward presentation of the basic constructions and terminology of category theory, including limits, functors, natural transformations, adjoints, and cartesian closed categories. Four case studies illustrate applications of category theory to programming language design, semantics, and the solution of recursive domain equations. A brief literature survey offers suggestions for further study in more advanced texts. Contents Tutorial • Applications • Further Reading