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Author: Peter J. Cameron Publisher: Springer Science & Business Media ISBN: 1447105893 Category : Mathematics Languages : en Pages : 191
Book Description
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.
Author: Peter J. Cameron Publisher: Springer Science & Business Media ISBN: 1447105893 Category : Mathematics Languages : en Pages : 191
Book Description
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.
Author: Peter J. Cameron Publisher: Springer Science & Business Media ISBN: 9781852330569 Category : Mathematics Languages : en Pages : 196
Book Description
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.
Author: Robert R. Stoll Publisher: Courier Corporation ISBN: 0486139646 Category : Mathematics Languages : en Pages : 516
Book Description
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.
Author: F. William Lawvere Publisher: Cambridge University Press ISBN: 9780521010603 Category : Mathematics Languages : en Pages : 280
Book Description
In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.
Author: B. Jacobs Publisher: Gulf Professional Publishing ISBN: 9780444508539 Category : Computers Languages : en Pages : 784
Book Description
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.
Author: Moshe Machover Publisher: Cambridge University Press ISBN: 9780521479981 Category : Mathematics Languages : en Pages : 304
Book Description
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.
Author: André Joyal Publisher: Cambridge University Press ISBN: 9780521558303 Category : Mathematics Languages : en Pages : 136
Book Description
This book offers a new algebraic approach to set theory. The authors introduce a particular kind of algebra, the Zermelo-Fraenkel algebras, which arise from the familiar axioms of Zermelo-Fraenkel set theory. Furthermore, the authors explicitly construct these algebras using the theory of bisimulations. Their approach is completely constructive, and contains both intuitionistic set theory and topos theory. In particular it provides a uniform description of various constructions of the cumulative hierarchy of sets in forcing models, sheaf models and realizability models. Graduate students and researchers in mathematical logic, category theory and computer science should find this book of great interest, and it should be accessible to anyone with a background in categorical logic.
Author: Charles C Pinter Publisher: Courier Corporation ISBN: 0486497089 Category : Mathematics Languages : en Pages : 259
Book Description
"This accessible approach to set theory for upper-level undergraduates poses rigorous but simple arguments. Each definition is accompanied by commentary that motivates and explains new concepts. A historical introduction is followed by discussions of classes and sets, functions, natural and cardinal numbers, the arithmetic of ordinal numbers, and related topics. 1971 edition with new material by the author"--
Author: Peter J. Cameron
Author: Peter J. Cameron
Author: Peter J. Cameron
Author: Robert R. Stoll
Author: Tom Leinster
Author: F. William Lawvere
Author: B. Jacobs
Author: Moshe Machover
Author: 
Author: André Joyal
Author: Charles C Pinter