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I would first like to apologize for posting a question similar to others previously posted.

I've already had an undergraduate course in logic but we did not use a standard text. Rather, we discussed the main ideas of propositional logic, predicate logic, and a bit on undecidability; though nothing too deep. Consequently, I'm seeking a text to advance my understanding via self-studies.

I've skimmed through some of the logic texts by Enderton, Ebbinghaus Flum Thomas, Wolfgang, and Shoenfield at my school's library and they all seem manageable.

Personally, I'm leaning towards Shoenfield or EFT.

My concerns/questions are:

1.) Are the notations of these old texts severely outdated?

2.) Do they cover distinct systems?

3.) Are there any conventions that are simply just not used anymore with the older texts?

4.) Would these (any) make a good book for an intermediate level? Are there any other good books you would recommend instead?

Edit: I should mention that my undergraduate course covered very little compared to any of the texts. That is, we skimmed over model theory and we took some things for granted (some of which were spontaneous (ex: Skolem's Theorem)) since set theory was not required.

Thanks.

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  • $\begingroup$ Personally, after having an undergraduate course in logic, I don't really see much benefit in reading a more technical book in general logic. I would recommend looking at the introductory graduate texts in the main sub-areas of mathematic logic: Model Theory, Computability Theory, and Set Theory. $\endgroup$
    – William
    Aug 18, 2013 at 2:06
  • $\begingroup$ Take note of the above edit. If you still believe otherwise, what are some good introductory texts in proof theory and model theory? (I'm already doing coursework in set theory and on recursion/computation) $\endgroup$
    – Klungo
    Aug 18, 2013 at 2:25
  • $\begingroup$ Also take a look at Peter Hinman's book "Fundamentals of Mathematical Logic." It's based on graduate courses in general logic, model theory, set theory, and recursion theory that Peter taught at the University of Michigan. [In case you didn't check my profile or otherwise find out: I'm also at the University of Michigan, so increase or decrease the weight you assign to my comment accordingly.] $\endgroup$
    – Andreas Blass
    Aug 18, 2013 at 2:43
  • $\begingroup$ I've actually been wanting to look into that text, but there isn't copy at the library nor could I see the preview on Amazon. It's the same one used in my school's graduate course. It's rather pricey though! $\endgroup$
    – Klungo
    Aug 18, 2013 at 3:03
  • $\begingroup$ I also like Shoenfield. But, you could check out "Introduction to Mathematical Logic" by Elliott Mendelson. $\endgroup$
    – J126
    Aug 18, 2013 at 3:17

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I'd say that both Shoenfield and EFT are unnecessarily tough going for a near beginner. So what instead? There is a 60 page Teach Yourself Logic Study Guide downloadable from http://www.logicmatters.net/students/tyl/ which gives extensive advice about what is available covering different areas of mathematical logic at different levels and which should be helpful.

[Don't be put off by the fact that the Guide started life written for graduate philosophy students: later versions are for mathematicians too. But the original target audience explains why the Guide does make a big thing about accessibility for self-teaching purposes.]

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    $\begingroup$ If there are no exercises with answers than this book does not do "big thing about accessibility for self-teaching purposes", certainly. $\endgroup$
    – Trismegistos
    Aug 19, 2013 at 6:44
  • $\begingroup$ The Guide isn't a book, it is an annotated reading list. $\endgroup$
    – Peter Smith
    Aug 19, 2013 at 7:21
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    $\begingroup$ So implication I provided is vacuously true ;D. $\endgroup$
    – Trismegistos
    Aug 19, 2013 at 10:55

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