most recent 30 from http://mathoverflow.net 2013-05-19T06:14:05Z http://mathoverflow.net/feeds/question/95611 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/95611/books-on-logic-for-someone-aiming-to-go-to-grad-school-in-the-field qwerty 2012-04-30T20:08:19Z 2012-04-30T20:15:41Z

<p>I have taken two introductory courses on logic. One was an undergraduate level and the second one was at the graduate level. Both used a set of notes written by the instructor. I'm thinking about graduate school in the field and would like to spend my next summer reading more about logic.</p> <p>What I'm looking at is a good list of rigorous graduate level textbooks on the most important topics in logic that would get one started and which would provide a good foundation for graduate level studies. I have the whole summer and my senior year to prepare.</p> <p>Which books would you recommend? My plan at this point would be to read a rigorous graduate level textbook on basic logic and then one on model theory. The ones that I've looked at are: </p> <p>Manin, A Course in Mathematical Logic for Mathematicians</p> <p>Marker, Model Theory: An Introduction</p> <p>Would this be a nice place to start or are there better options?</p>

http://mathoverflow.net/questions/95611/books-on-logic-for-someone-aiming-to-go-to-grad-school-in-the-field/95612#95612 Andreas Blass 2012-04-30T20:15:41Z 2012-04-30T20:15:41Z

<p>For set theory, I recommend Drake's "Set theory: An introduction to large cardinals" (which also contains a good treatment of various other parts of set theory, before concentrating on large cardinals) and Kunen's "Set theory: An introduction to independence proofs." The "bible" of set theory is Jech's "Set Theory" but I think it may be easier to learn from Drake and Kunen first. [Do you get the impression that set theorists are not very creative when it comes to book titles?]</p> <p>For logic in general, Shoenfield's "Mathematical Logic" covers an amazing amount of material in rather few pages. Most of it is great (if you do the exercises, into which a lot of material has been squeezed) but I wouldn't recommend his approach to constructibility and forcing --- use Kunen instead.</p>