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Undergraduate (not graduate, the linked post is a bit too advanced) here looking for a logic textbook reference. Here’s a bit about me:

  • Experience with basic proof-based linear algebra (Linear Algebra Done Right and other texts)
  • Basic Analysis (I will have gone through Tao’s Analysis I when I get to the textbook on logic)
  • Diffeq and Calc 3
  • I do not have any experience with set theory. I might read through Halmos’ book for a brief intro if you all think that might be useful, but will hold off on more substantial reading, like Enderton’s book, until later (I also know that Enderton has a logic book, but don’t know anything of it).

I am looking for an introductory textbook that is as comprehensive as possible for the prerequisites I have under my belt. I don’t mind terseness or difficulty as long as there aren’t math concepts I literally don’t know and would need to reference another text for. I know Enderton’s book is good and was leaning to that, but would love other recommendations.

RD Healthcare
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    @Another User: I suspect the books at the MSE question you cited are too advanced for the OP, whose level seems roughly somewhere at the U.S. 2nd undergraduate year. Better (besides Enderton's book) would probably be Logic for Mathematicians by Hamilton OR Propositional and Predicate Calculus. A Model of Argument by Goldrei OR An Introduction to Formal Logic by Peter Smith. – Dave L. Renfro Mar 19 '24 at 10:00
  • Thanks. Is there one of these that stands out as more comprehensive or of better quality? Is not, that is also alright. – RD Healthcare Mar 19 '24 at 15:42
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    Peter Smith has written an entire book about the literature on logic textbooks. You can get it for a very fair price on amazon and it might contain what you are looking for. – Cornman Mar 19 '24 at 15:45
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    Apparently you get it for free here: https://www.logicmatters.net/resources/pdfs/LogicStudyGuide.pdf Seems to be with consent of the author. – Cornman Mar 19 '24 at 15:46
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    more comprehensive or of better quality? --- The problem with "more comprehensive" is that it is heavily dependent on your background. I spent a few months in Fall 2011 going back over some introductory logic (described here, with some texts mentioned). When I was an undergraduate (late 1970s) the "comprehensive standard text" was probably Mathematical Logic by Shoenfield, and often mentioned were the two Kleene books mentioned in this MSE answer. – Dave L. Renfro Mar 19 '24 at 16:06
  • I suppose I could modify my question. Of the books you recommended (Enderton, Hamiltons, Smith, and Goldrei), which one “gets the farthest” into the subject? – RD Healthcare Mar 19 '24 at 16:20
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    which one “gets the farthest” into the subject? --- Probably Enderton, but if this book is "within your reach", then you should also consider Boolos/Burgess/Jeffrey and Ebbinghaus/Flum/Thomas and van Dalen. And if you have the time to devote to it, An Introduction to Mathematical Logic by Hodel is especially thorough and detailed, while also being roughly at the same "advanced undergraduate level" as the other books. – Dave L. Renfro Mar 20 '24 at 08:00
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    Regarding Hodel's book, Hodel was a colleague of Shoenfield at Duke University ("was" because Shoenfield died in 2000) and Hodel's book is a more student-friendly reworking of much of Shoenfield's famous book (famous from both a scholarly point of view and from a "difficult for beginners" point of view). – Dave L. Renfro Mar 20 '24 at 08:08

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