Smullyan R. A Beginner's Guide to Mathematical Logic 2014

Textbook in PDF format

Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems.
Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. 2014 edition.
General Background.
Genesis.
Infinite Sets.
Some Problems Arise!
Further Background.
Propositional Logic.
Beginning Propositional Logic.
Propositional Tableaux.
Axiomatic Propositional Logic.
First-Order Logic.
Beginning First-Order Logic.
First-Order Logic: Main Topics.
The Incompleteness Phenomenon.
Incompleteness in a General Setting.
Elementary Arithmetic.
Formal Systems.
Peano Arithmetic.
Further Topics