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!
"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.