Books for Improving Understanding of Mathematical Logic and Set Theory for IIT JAM Mathematics Paper

1. "Mathematical Logic" by George Tourlakis:
This book provides a comprehensive introduction to mathematical logic, covering topics such as propositional and first-order logic, proof theory, and model theory. It is suitable for beginners and covers the fundamental concepts and techniques required for understanding mathematical logic. The book also includes numerous examples and exercises to reinforce the concepts.

2. "Set Theory: An Introduction to Independence Proofs" by Kenneth Kunen:
This book focuses on set theory and independence proofs, which are important topics in mathematical logic. It covers topics such as axiomatic set theory, cardinal and ordinal numbers, and the constructible universe. The book is written in a clear and concise manner, making it suitable for self-study. It also includes exercises at the end of each chapter to test your understanding.

3. "A Course in Mathematical Logic" by Yu. I. Manin:
This book provides a comprehensive introduction to mathematical logic, presenting the basic concepts and techniques in a clear and concise manner. It covers topics such as propositional and predicate logic, model theory, and Gödel's incompleteness theorems. The book also includes numerous examples and exercises to reinforce the concepts.

4. "Introduction to Mathematical Logic" by Elliott Mendelson:
This book offers a comprehensive introduction to mathematical logic, covering topics such as propositional and predicate logic, proof theory, and model theory. It provides clear explanations and examples, making it suitable for self-study. The book also includes numerous exercises to practice and reinforce the concepts learned.

5. "Set Theory and Logic" by Robert R. Stoll:
This book provides an introduction to set theory and mathematical logic. It covers topics such as sets, relations, functions, propositional and predicate logic, and proofs. The book includes numerous examples and exercises to help develop a deeper understanding of the concepts. It also provides historical background and motivation for the topics discussed.

6. "Axiomatic Set Theory" by Patrick Suppes:
This book presents an axiomatic approach to set theory, covering topics such as well-orderings, ordinal and cardinal numbers, and the axiom of choice. It provides a rigorous treatment of the subject and includes exercises to test and reinforce your understanding. The book is suitable for advanced students who already have a basic understanding of set theory.

7. "Introduction to Set Theory" by Karel Hrbacek and Thomas Jech:
This book provides a comprehensive introduction to set theory, covering topics such as sets, functions, relations, and cardinals. It also includes a chapter on forcing, which is an important technique in set theory. The book is suitable for beginners and includes numerous examples and exercises to reinforce the concepts.

These books cover the fundamental concepts and techniques of mathematical logic and set theory, making them suitable for preparing for the IIT JAM Mathematics Paper. They provide clear explanations, examples, and exercises to help you develop a deep understanding of the subject. Regular practice with the exercises will also help you improve your problem-solving skills, which are essential for success in the exam.