Mathematical Logic: An Introduction

Daniel Cunningham

Published by De Gruyter 2023

Mathematical Logic

An Introduction

Daniel Cunningham

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110782073

Overview
Contents

About this book

Mathematical Logic: An Introduction is a textbook that uses mathematical tools to

investigate mathematics itself. In particular, the concepts of proof and truth are examined.

The book presents the fundamental topics in mathematical logic and presents clear and

complete proofs throughout the text. Such proofs are used to develop the language of

propositional logic and the language of first-order logic, including the notion of a formal

deduction. The text also covers Tarski’s definition of truth and the computability concept.

It also provides coherent proofs of Godel’s completeness and incompleteness theorems.

Moreover, the text was written with the student in mind and thus, it provides an accessible

introduction to mathematical logic. In particular, the text explicitly shows the reader

how to prove the basic theorems and presents detailed proofs throughout the book. Most

undergraduate books on mathematical logic are written for a reader who is well-versed

in logical notation and mathematical proof. This textbook is written to attract a wider

audience, including students who are not yet experts in the art of mathematical proof.

This text written with the student in mind provides an accessible introduction to logic, explicitly showing the reader how to produce and compose the proofs of the basic theorems in mathematical logic through numerous examples and exercises.

Author information

Daniel W. Cunningham is a Professor Emeritus of Mathematics at SUNY Buffalo State, a

campus of the State University of New York. Daniel received a Ph.D. in Mathematics from

UCLA, specializing in mathematical logic. He currently teaches at California State University

at Fresno. Cunningham’s research focus is in set theory, and has recently published

two research papers and two textbooks

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Acknowledgments Publicly Available Download PDF	IX
Contents Publicly Available Download PDF	XI
1 Basic set theory and basic logic Requires Authentication Unlicensed Licensed Download PDF	1
2 Propositional logic Requires Authentication Unlicensed Licensed Download PDF	27
3 First-order logic Requires Authentication Unlicensed Licensed Download PDF	52
4 Soundness and completeness Requires Authentication Unlicensed Licensed Download PDF	119
5 Computability Requires Authentication Unlicensed Licensed Download PDF	148
6 Undecidability and incompleteness Requires Authentication Unlicensed Licensed Download PDF	205
Bibliography Requires Authentication Unlicensed Licensed Download PDF	249
Symbol Index Requires Authentication Unlicensed Licensed Download PDF	251
Subject Index Requires Authentication Unlicensed Licensed Download PDF	253

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Senior and first year graduate level students taking a course in logic.
Pages
- Front matter: 14
- Main content: 256
Illustrations
- Illustrations: 30
Keywords: Mathematical logic; logic of the first order; logic of the second order; deductive reasoning.

eBook

Published: May 22, 2023
ISBN: 9783110782073

Paperback

Published: May 22, 2023
ISBN: 9783110782011