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.
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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. 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.
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4 of 4 people found the following review helpful:
4.0 out of 5 stars
Why is this out of print?,
By † (United States) - See all my reviews
This review is from: Friendly Introduction to Mathematical Logic, A (Hardcover)
The impossible goal of this text is to start from scratch and then cover both incompleteness theorems in a single semester, and under his presentation it would almost be manageable. This is by far the best written text on predicate calculus I have read. Kaye and Goldrei can't really compare, as they contain less material and what they do cover isn't done quite as well. Enderton on the other hand covers more than Leary, but is much more dense and would not serve as well as an introduction.
The main drawback of the book is how much effort the author put into making it fit into a single semester. There is a lot of fascinating material that could have been covered in greater depth than is done. It is worth noting that he almost completely skips over propositional calculus, so if you find yourself struggling at the beginning of the book you may want to read up on that subject in another text (the first half of Goldrei would do nicely). Also the section on the second incompleteness theorem is extremely rushed; some of the properties of peano arithmetic used for the proof are not proven. Still, it's better than the other options I've seen. You would think with all the mediocre mathematics texts Dover picks up they would have found this gem. Beyond knowing the rudiments of naïve set theory, prerequisites should not be much of a concern.
8 of 10 people found the following review helpful:
5.0 out of 5 stars
Most Accessible Undergraduate Text Covering Incompleteness,
By
This review is from: Friendly Introduction to Mathematical Logic, A (Hardcover)
I have used this text in both graduate and undergraduate courses as well as tutorials and independent studies. It is the best text for a one semester course that introduces formal logic and has as its goal the Incompleteness Theorems of Godel. Students have reported it to be very readable and the array of exercises is excellent. Moreover, the author is a really nice fellow.
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