Fundamentals of Mathematical Logic

by Peter G. Hinman

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.

Genres: Mathematics, Logic, Philosophy

894 pages, Hardcover

First published November 15, 2005

Reviews

[Adam · Rating 4 out of 5]

It is among my favorite Mathematical Logic textbooks. It is imperfect, but in my opinion, less so than all other Mathematical Logic textbooks that I've read (Enderton, Kristiansen and Leary, Cori and Lascar, Mendelson, Manin, Ebbinghaus). I find its presentation direct and efficient, while still setting its goals more-or-less broad enough. It definitely lacks in proof theory, as the author admits in the forward, but no text can cover everything and there are whole books dedicated to proof theory, so I don't see this as a terrible deficiency since you can just read another book on this subject. It also doesn't present model theory in such a way that you will be lost if you don't have a deep background in abstract algebra. It introduces the set theoretic tools that you need as self-contained, so much so that I feel like this would be a pretty easy warm-up for a future course in Set Theory.

I decided to make a video companion series, to talk through the ideas of the text, here: https://youtube.com/playlist?list=PLc...