Mathematical Logic: A Course With Exercises – Propositional Calculus, Boolean Algebras, Predicate Calculus & Completenes

Introduction

Mathematical logic is the bedrock of all rigorous reasoning, yet it often intimidates students with its abstract symbols and dense theorems. Mathematical Logic: A Course With Exercises : Propositional Calculus, Boolean Algebras, Predicate Calculus by René Cori breaks down these barriers, offering a clear and systematic journey into the heart of logic. Published by Oxford University Press, this hardcover volume is tailored for advanced undergraduate students in India and around the world who want to build a solid foundation in formal logic. Whether you are preparing for competitive exams, pursuing a degree in mathematics or computer science, or simply fascinated by the structure of truth, this book will guide you step by step through propositional calculus, Boolean algebras, and predicate calculus—all the way to completeness theorems.

Book Overview

This first part of a two-volume course focuses on the core pillars of mathematical logic. The author, René Cori, a respected French mathematician and logician, presents the subject with exceptional clarity. The book begins with propositional calculus, introducing syntax, semantics, and natural deduction. It then explores Boolean algebras, showing how algebraic structures model logical operations. The later chapters delve into predicate calculus, covering quantifiers, models, and the famed completeness theorems. Every chapter is accompanied by a rich set of exercises, and the volume concludes with detailed answers to all problems. This makes it an ideal self-study resource for Indian students who need to master logic without constant external guidance.

Key Highlights

• Comprehensive coverage of propositional calculus, Boolean algebras, predicate calculus, and completeness theorems in one volume.
• Over 200 graded exercises with complete solutions at the end of the book—perfect for independent practice.
• Clear, step-by-step proofs that build from basic definitions to advanced results like Gödel's completeness theorem.
• Focus on models and semantics, making abstract concepts tangible and intuitive.
• Hardcover edition from Oxford University Press, durable for years of reference and study.

Inside the Book

The book is structured in three major parts. Part I covers propositional calculus: truth tables, tautologies, logical equivalence, and natural deduction systems. Part II introduces Boolean algebras, connecting logic to algebra with lattice theory and Stone's representation theorem. Part III presents predicate calculus: first-order languages, structures, satisfaction, and the completeness theorem. Each chapter begins with motivating examples and ends with a summary and exercises. The solutions section is exceptionally thorough, showing not just the answer but the reasoning process. This is a textbook that rewards careful reading and active problem-solving.

Key Topics

• Propositional logic: syntax, semantics, truth tables, natural deduction
• Boolean algebras: axioms, homomorphisms, filters, ultrafilters
• Predicate calculus: quantifiers, first-order languages, models
• Completeness theorems: Henkin's method, compactness, Löwenheim-Skolem theorems
• Formal proofs and soundness
• Applications to mathematics and computer science

Reader Benefits

• Build rigorous reasoning skills essential for advanced mathematics and theoretical computer science.
• Gain confidence in handling formal proofs and abstract structures.
• Prepare for higher studies in logic, set theory, or philosophy of mathematics.
• Self-paced learning with fully solved exercises—no need for a tutor.
• Deepen your understanding of foundational concepts that underpin all of mathematics.

Learning Outcomes

By the end of this book, readers will be able to: construct and evaluate propositional formulas; prove tautologies using natural deduction; analyze Boolean algebras and their properties; work with first-order predicate logic; build models for logical theories; prove completeness and compactness theorems; and apply these tools to solve complex problems in mathematics and logic. The exercises ensure that theoretical knowledge is immediately tested and reinforced.

Who Should Read

This book is ideal for advanced undergraduate students in mathematics, computer science, or philosophy. It is also suitable for postgraduate students who need a refresher in formal logic, and for self-learners with a strong background in basic mathematics. Indian students preparing for the NBHM, ISI, CMI, or JRF exams will find the depth and clarity particularly valuable. Lecturers and teachers can use it as a primary text for a semester-long course on mathematical logic.

About the Author

René Cori is a distinguished French mathematician and logician, known for his contributions to model theory and proof theory. He has taught at the Université Paris Diderot and has authored several influential textbooks. His writing style is precise yet accessible, making complex ideas understandable without sacrificing rigor. This book reflects decades of teaching experience and a deep passion for logical foundations.

About the Publisher

Oxford University Press (OUP) is one of the oldest and most respected academic publishers in the world. Known for its rigorous editorial standards and scholarly excellence, OUP produces textbooks that are trusted by universities globally. This hardcover edition is printed on high-quality paper with a durable binding, ensuring it withstands frequent use in libraries and personal collections.

Conclusion

Mathematical Logic: A Course With Exercises : Propositional Calculus, Boolean Algebras, Predicate Calculus is more than a textbook—it is a companion for anyone serious about understanding the logical foundations of mathematics. With its clear exposition, abundant exercises, and complete solutions, it is the perfect resource for Indian students and academics. Add this essential volume to your library and unlock the power of logical reasoning. Order your copy from Bookshops.in today and begin your journey into the elegant world of mathematical logic.