Sets Logic And Categories

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Sets, Logic and Categories

Peter J. Cameron
Sets Logic and Categories Book PDF

Author : Peter J. Cameron
Publisher : Springer Science & Business Media
Page : 191 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105893

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Sets, Logic and Categories by Peter J. Cameron Pdf

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.

Set Theory, Logic and Their Limitations

Moshe Machover
Set Theory Logic and Their Limitations Book PDF

Author : Moshe Machover
Publisher : Cambridge University Press
Page : 304 pages
File Size : 47,7 Mb
Release : 1996-05-23
Category : Mathematics
ISBN : 0521479983

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Set Theory, Logic and Their Limitations by Moshe Machover Pdf

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.

Elements of Logic via Numbers and Sets

D.L. Johnson
Elements of Logic via Numbers and Sets Book PDF

Author : D.L. Johnson
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447106036

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Elements of Logic via Numbers and Sets by D.L. Johnson Pdf

In mathematics we are interested in why a particular formula is true. Intuition and statistical evidence are insufficient, so we need to construct a formal logical proof. The purpose of this book is to describe why such proofs are important, what they are made of, how to recognize valid ones, how to distinguish different kinds, and how to construct them. This book is written for 1st year students with no previous experience of formulating proofs. Dave Johnson has drawn from his considerable experience to provide a text that concentrates on the most important elements of the subject using clear, simple explanations that require no background knowledge of logic. It gives many useful examples and problems, many with fully-worked solutions at the end of the book. In addition to a comprehensive index, there is also a useful `Dramatis Personae` an index to the many symbols introduced in the text, most of which will be new to students and which will be used throughout their degree programme.

Basic Category Theory

Tom Leinster
Basic Category Theory Book PDF

Author : Tom Leinster
Publisher : Cambridge University Press
Page : 193 pages
File Size : 52,8 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9781107044241

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Basic Category Theory by Tom Leinster Pdf

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

Set Theory and Logic

Robert R. Stoll
Set Theory and Logic Book PDF

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 42,5 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486139647

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Set Theory and Logic by Robert R. Stoll Pdf

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.

Categorical Logic and Type Theory

B. Jacobs
Categorical Logic and Type Theory Book PDF

Author : B. Jacobs
Publisher : Gulf Professional Publishing
Page : 784 pages
File Size : 50,9 Mb
Release : 2001-05-10
Category : Computers
ISBN : 0444508538

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Categorical Logic and Type Theory by B. Jacobs Pdf

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.

Linear Representations of Partially Ordered Sets and Vector Space Categories

Daniel Simson
Linear Representations of Partially Ordered Sets and Vector Space Categories Book PDF

Author : Daniel Simson
Publisher : CRC Press
Page : 516 pages
File Size : 55,8 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 2881248284

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Linear Representations of Partially Ordered Sets and Vector Space Categories by Daniel Simson Pdf

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.

Sets for Mathematics

F. William Lawvere,Robert Rosebrugh
Sets for Mathematics Book PDF

Author : F. William Lawvere,Robert Rosebrugh
Publisher : Cambridge University Press
Page : 280 pages
File Size : 46,8 Mb
Release : 2003-01-27
Category : Mathematics
ISBN : 0521010608

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Sets for Mathematics by F. William Lawvere,Robert Rosebrugh Pdf

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

Category Theory in Context

Emily Riehl
Category Theory in Context Book PDF

Author : Emily Riehl
Publisher : Courier Dover Publications
Page : 272 pages
File Size : 51,9 Mb
Release : 2017-03-09
Category : Mathematics
ISBN : 9780486820804

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Category Theory in Context by Emily Riehl Pdf

Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Categories for Types

Roy L. Crole
Categories for Types Book PDF

Author : Roy L. Crole
Publisher : Cambridge University Press
Page : 362 pages
File Size : 41,8 Mb
Release : 1993
Category : Computers
ISBN : 0521457017

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Categories for Types by Roy L. Crole Pdf

This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.

Elements of ?-Category Theory

Emily Riehl,Dominic Verity
Elements of Category Theory Book PDF

Author : Emily Riehl,Dominic Verity
Publisher : Cambridge University Press
Page : 781 pages
File Size : 43,7 Mb
Release : 2022-02-10
Category : Mathematics
ISBN : 9781108837989

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Elements of ?-Category Theory by Emily Riehl,Dominic Verity Pdf

This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.

Sets, Logic, Computation

Richard Zach
Sets Logic Computation Book PDF

Author : Richard Zach
Publisher : Unknown
Page : 418 pages
File Size : 43,6 Mb
Release : 2021-07-13
Category : Electronic
ISBN : 9798536395509

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Sets, Logic, Computation by Richard Zach Pdf

A textbook on the semantics, proof theory, and metatheory of first-order logic. It covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic. It is based on the Open Logic project, and available for free download at slc.openlogicproject.org.

Set Theory

Daniel W. Cunningham
Set Theory Book PDF

Author : Daniel W. Cunningham
Publisher : Cambridge University Press
Page : 265 pages
File Size : 41,6 Mb
Release : 2016-07-18
Category : Mathematics
ISBN : 9781107120327

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Set Theory by Daniel W. Cunningham Pdf

Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.

An Invitation to Applied Category Theory

Brendan Fong,David I. Spivak
An Invitation to Applied Category Theory Book PDF

Author : Brendan Fong,David I. Spivak
Publisher : Cambridge University Press
Page : 351 pages
File Size : 40,7 Mb
Release : 2019-07-18
Category : Computers
ISBN : 9781108482295

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An Invitation to Applied Category Theory by Brendan Fong,David I. Spivak Pdf

Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.

Category Theory

Steve Awodey
Category Theory Book PDF

Author : Steve Awodey
Publisher : Oxford University Press
Page : 328 pages
File Size : 51,9 Mb
Release : 2010-06-17
Category : Mathematics
ISBN : 9780199587360

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Category Theory by Steve Awodey Pdf

A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems (with full proofs), as well as numerous examples and exercises.