This introductory graduate text covers modern mathematical logic from propositional, first-order and infinitary logic and Gödel's Incompleteness Theorems to extensive introductions to set theory, model theory and recursion (computability) theory. Based on the author's more than 35 years of teaching experience, the book develops students' intuition by presenting complex ideas in the simplest context for which they make sense. The book is appropriate for use as a classroom text, for self-study, and as a reference on the state of modern logic.
Table of Contents
Introduction, 1 Propositional Logic and Other Fundamentals, 2 First-Order Logic, 3 Completeness and Compactness, 4 Incompleteness and Undecidability, 5 Topics in Definability, 6 Set Theory, 7 Model Theory, 8 Recursion Theory. References.
Peter G. Hinman earned his B.A. in mathematics from Harvard University in 1959. He studied mathematics at the graduate level in Berkeley at the University of California. In 1966, under the guidance of Professor John Addison, he received his Ph.D. in Mathematical Logic with a particular focus on Recursion Theory. He is currently a professor at the University of Michigan where he has taught since 1966 and advised seven successful Ph.D. students. In 1978 he published his first book Recursion-Theoretic Hierarchies.
" expect this book to become the standard graduate logic text for the new century, based on the enthusiastic reception from students in our course last year."" -Doug Cenzer, University of Florida, July 2005
book is the long awaited successor to Shoenfield's book. At last under one cover is all one needs for an advanced introduction to mathematical logic. I will recommend it to all my beginning students."" -Gerald Sacks, Harvard University, November 2005
""The book develops students' intuition by presenting complex end difficult ideas in the simplest context for which they make sense. Each part of the text contains useful remarks, illustrative examples ond related exercises ... the author's style is quite clear and approachable. No previous experience with logic is presumed, only the maturity and capacity for abstraction. Consequently, this book seems to be ideal to graduate students of both mathematics ond theoretical computer science, as well as to students of philosophy and a large circle of specialists working in the field of mathematical logic."" -Branislav Boricic, Zentralblatt MATH, July 2006
""Based on the author's more than thirty-five years of teaching experience at the University of Michigan, and nearly twenty years in the writing, this book incorporates what he has leamed about enabling students with varying levels of interest and ability to come to a deep understanding of this beautiful subject."" -Peter Fillmore, CMS, February 2007
""Based on the author's more than thirty-five years of teaching experience at the University of Michigan, and nearly twenty years in the writing, this book incorporates what he has learned about enabling 'students with varying levels of interest and ability to come to a deep understanding of this beautiful subject.' Among the testimonials from users: At last under one cover is all one needs for an advanced introduction to mathematical logic (Gerald Sacks, Harvard)."" -Canadian Mathematical Society, February 2007"