Customer Reviews

The Mathematics of Logic: A Guide to Completeness Theorems and their Applications

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First off, this book has a wider and more interesting variety of formal systems than the other logic books I have gone through. What's more, Kaye's formal systems are much easier and more intuitive. Sadly, the text is absolutely riddled with errors. Check the errata on his site and you will see two or three corrections, read the book yourself and you will find that that list is far from complete. Most of them are just minor annoyances, but some of them really cause a lot of confusion. One of the questions was so bad that even my professor could not find a way to salvage it. Also, Kaye seems at times somewhat confused about his target audience. He feels the need to define simple things such as countability, but expects the reader to have decent exposure to both algebra and topology (I know little about either). Chapter eight is pretty much incomprehensible if you're not good with algebra, fortunately that chapter is optional. I also found sections 10.4, 11.3 and 12.3 (all optional) too difficult for me to get through. Overall I would say the book has a lot of potential, but I can't recommend it to anyone in the condition it's in now, especially if you don't have a professor to help walk you through it. Does not cover incompleteness.