I have been navigating in this "foundational world" of mathematics for a while now ( but certainly not long enough and not deep enough ) and have read a bit about many different topics : set theory, logic, Godel completeness and incompleteness theorems , model theory and proof theory.

I was wondering if anyone has a recommendation of a resource ( site, article, notes but mainly a book ) that gives a shallow overview of this foundational area of mathematics (Mathematical Logic) in a way to relate and show the connection between those many of the subjects i mentioned, kind of giving an introduction to each area.

I find that books of a certain topic are too specific ( and with the right reason ) and end up not providing the at least "basic" big picture of Foundational Mathematics I wish to have before delving deeper in my studies.

Thanks a lot!

  • 1
    $\begingroup$ I don't know about a specific book. But I think that any book covering the basics of first-order logic, and a book covering the basics of set theory, and then some time to connect the missing dots on your own should suffice. $\endgroup$
    – Asaf Karagila
    Commented Apr 27, 2014 at 15:01
  • 1
    $\begingroup$ I suggest you two recent books : Pavel Pudlak, Logical Foundations of Mathematics and Computational Complexity (2013) and Kenneth Kunen, The Foundations of Mathematics (2009). $\endgroup$ Commented Apr 27, 2014 at 17:08
  • 1
    $\begingroup$ I suggest also the books referenced by Peter Smith in this post for the historical background. $\endgroup$ Commented Apr 27, 2014 at 17:09
  • $\begingroup$ Thanks for those suggestions, you two :) $\endgroup$
    – nerdy
    Commented Apr 27, 2014 at 19:43
  • 1
    $\begingroup$ One book that I've found very useful and which introduced me to this subject is "Foundations of Set Theory" by Fraenkel, Bar-Hillel and Levy. The book is not too specific and introduces different systems. $\endgroup$ Commented Apr 28, 2014 at 2:49

1 Answer 1


"Introduction to Metamathematics" and the even more basic "Mathematical Logic" by Stephen Cole Kleene both give a very good overview of the foundational area of mathematics and provided the basic big picture for me.


You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .