At the very beginning of Feferman's Arithmetization of metamathematics in a general setting it can be read: The method of arithmetization, as developed by Gödel, exploits the possibility of ...
I am reading Bjorn Poonen's very nice survey on Hilbert's Tenth problem (http://www-math.mit.edu/~poonen/papers/uniform.pdf), and while I believe I understand the mathematics well, I have widespread ...
Metamathematics has a reasonably clear connotation, enough to have a Wikipedia page, with Gödel, Tarski, and Turing playing leading roles; Kleene's book (Introduction to Metamathematics (Amazon link));...
Is it possible to prove $Con(ZFC) \rightarrow Con(ZFC + \neg CH)$ purely within ZFC? To prove this (using forcing) one seems to need a countable transitive model of ZFC. The texts I am reading avoid ...