Sets, Logic and Categories
Sets, Logic and Categories

Author: Peter J. Cameron

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 191

ISBN-13: 1447105893

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Set theory, logic and category theory lie at the foundations of mathematics, and have a dramatic effect on the mathematics that we do, through the Axiom of Choice, Gödel's Theorem, and the Skolem Paradox. But they are also rich mathematical theories in their own right, contributing techniques and results to working mathematicians such as the Compactness Theorem and module categories. The book is aimed at those who know some mathematics and want to know more about its building blocks. Set theory is first treated naively an axiomatic treatment is given after the basics of first-order logic have been introduced. The discussion is su pported by a wide range of exercises. The final chapter touches on philosophical issues. The book is supported by a World Wibe Web site containing a variety of supplementary material.

Linear Representations of Partially Ordered Sets and Vector Space Categories
Linear Representations of Partially Ordered Sets and Vector Space Categories

Author: Daniel Simson

Publisher: CRC Press

Published: 1993-01-01

Total Pages: 516

ISBN-13: 9782881248283

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This volume provides an elementary yet comprehensive introduction to representations of partially ordered sets and bimodule matrix problems, and their use in representation theory of algebras. It includes a discussion of representation types of algebras and partially ordered sets. Various characterizations of representation-finite and representation-tame partially ordered sets are offered and a description of their indecomposable representations is given. Auslander-Reiten theory is demonstrated together with a computer accessible algorithm for determining in decomposable representations and the Auslander-Reiten quiver of any representation-finite partially ordered set.

Set Theory and Logic
Set Theory and Logic

Author: Robert R. Stoll

Publisher: Courier Corporation

Published: 2012-05-23

Total Pages: 516

ISBN-13: 0486139646

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Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

Basic Category Theory
Basic Category Theory

Author: Tom Leinster

Publisher: Cambridge University Press

Published: 2014-07-24

Total Pages: 193

ISBN-13: 1107044243

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A short introduction ideal for students learning category theory for the first time.

Categorical Logic and Type Theory
Categorical Logic and Type Theory

Author: B. Jacobs

Publisher: Gulf Professional Publishing

Published: 2001-05-10

Total Pages: 784

ISBN-13: 9780444508539

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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.

Sets for Mathematics
Sets for Mathematics

Author: F. William Lawvere

Publisher: Cambridge University Press

Published: 2003-01-27

Total Pages: 280

ISBN-13: 9780521010603

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In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

An Invitation to Applied Category Theory
An Invitation to Applied Category Theory

Author: Brendan Fong

Publisher: Cambridge University Press

Published: 2019-07-18

Total Pages: 351

ISBN-13: 1108582249

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Category theory is unmatched in its ability to organize and layer abstractions and to find commonalities between structures of all sorts. No longer the exclusive preserve of pure mathematicians, it is now proving itself to be a powerful tool in science, informatics, and industry. By facilitating communication between communities and building rigorous bridges between disparate worlds, applied category theory has the potential to be a major organizing force. This book offers a self-contained tour of applied category theory. Each chapter follows a single thread motivated by a real-world application and discussed with category-theoretic tools. We see data migration as an adjoint functor, electrical circuits in terms of monoidal categories and operads, and collaborative design via enriched profunctors. All the relevant category theory, from simple to sophisticated, is introduced in an accessible way with many examples and exercises, making this an ideal guide even for those without experience of university-level mathematics.

Set Theory, Logic and Their Limitations
Set Theory, Logic and Their Limitations

Author: Moshe Machover

Publisher: Cambridge University Press

Published: 1996-05-23

Total Pages: 304

ISBN-13: 9780521479981

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This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Lectures in Logic and Set Theory: Volume 2, Set Theory
Lectures in Logic and Set Theory: Volume 2, Set Theory

Author: George Tourlakis

Publisher: Cambridge University Press

Published: 2011-07-21

Total Pages: 0

ISBN-13: 9780521168489

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Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).