Mathematical Logic

An Introduction

Daniel Cunningham

• Publisher: De Gruyter
• Year: 2023
• Print ISBN: 9783110782011
• eBook ISBN: 9783110782196
• Edition: 1
• Topic: Philosophy
• Subtopic: Algebra

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.

Table of contents

• Title Page
• Copyright
• Contents
• 1 Basic set theory and basic logic
• 2 Propositional logic
• 3 First-order logic
• 4 Soundness and completeness
• 5 Computability
• 6 Undecidability and incompleteness
• Subject Index