Friendly Introduction to Mathematical Logic, A

by Christopher C. Leary

This user-friendly introduction to the key concepts of mathematical logic focuses on concepts that are used by mathematicians in every branch of the subject. Using an assessible, conversational style, it approaches the subject mathematically (with precise statements of theorems and correct proofs), exposing readers to the strength and power of mathematics, as well as its limitations, as they work through challenging and technical results. KEY TOPICS : Structures and Languages. Deductions. Comnpleteness and Compactness. Incompleteness--Groundwork. The Incompleteness Theorems. Set Theory. : For readers in mathematics or related fields who want to learn about the key concepts and main results of mathematical logic that are central to the understanding of mathematics as a whole.

Genres: Philosophy, Mathematics, Logic, Nonfiction, Science, 21st Century

218 pages, Hardcover

First published December 8, 1999

Reviews

[Adam · Rating 3 out of 5]

I wouldn't call this downright friendly. It is more friendly than Mendelson's Mathematical Logic text, and it has the occasional, conversational tone to the reader, like somehow in a nonfiction book the author is managing to break a fourth wall. But the text still won't be accessible to the absolute mathematical novice, or even the reader with some mathematical background who goes into it not already having a concept of syntax and semantics and how these tend to get treated in Mathematical Logic.

Still I can't think of a text that tries to address these topics at this level, which is more friendly. So it's a good book.

[Arya · Rating 4 out of 5]

Great book for learning about Mathematical Logic, even if you have no background in symbolic logic! You just need an open mind, a lot of time, and maybe a friend that's willing to break things down for you. I only gave it four stars since it is still a little intimidating, but I would find it extremely hard to introduce all these topics in a simpler manner.

[Kevin Doran · Rating 1 out of 5]

I didn't get far into the book before putting it down. The review reflects my experience with the first 50 or so pages only. I can only image that there must be a better book.

For a book that is supposed to lay the foundations of mathematics, it is not very rigorous, and it is disorganized in its presentation. The foundations are poorly laid out. There are many ideas that are presented, like functions and sets and relations, that, while familiar to the reader, should not be used to set the foundation of the theory without some sort of formulation and specific definition. For example, without any specification of an axiom or justification, we are told to accept the existence of structures containing universes of objects and functions that map to each symbol of a language. While I can certainly accept the existence of such an object, I do not trust a presentation that doesn't justify or state such a claim as being assumed as an axiom. How much of set theory do we need to create a theory that is supposed to make claims about set theory? Maybe there is simple answer to this and I'm over reacting; but if there is such an answer, the author should have included it.

[Lucille Nguyen · Rating 3 out of 5]

Rather poorly organized and presented, some presentations of material were more intuitive than others, but overall other books on logic and mathematics are both more "friendly" (ironic, given the title) and comprehensive than this text.

[Navid Rashidian · Rating 4 out of 5]

An informative tour through some basic results in mathematical logic. The first three chapters cover first-order logic without wasting any pages on propositional logic (which may make everything harder if it's the first treatment of the subject you read) up to the foothills of model theory, e. g. the Löwenheim–Skolem theorems. Then there is a intermediary chapter on some technical details on coding which sets the ground for the next three chapters on Gödel's epoch-making incompleteness theorems. The first two prove the first incompleteness 'proof-theoretically' in a rather unusual way, and then state and prove some extensions of the theorem and some related results such as Tarski's undefinability of truth (which may come pretty handy if you would like to utter nonsense on how no one could ever define what is the truth). The second incompleteness is proved by assuming some derivability conditions about first-order Peano Arithmetics and only about PA, not in the general form. Then, there is an equally-approachable chapter on computability theory which is based on Kleene's μ-recursion and provides proofs to some basic results such as Kleene's Normal Form theorem, the undecidebility of the halting problem, the undecidability of the Entscheidungsproblem, the S-m-n theorem, Gödel's first incompleteness (again, via computability!), and Rice's theorem. If self-studying, the solutions in the back are pretty useful.