It seems that learning PA is necessary if you want to understand the relationship between logic and math. Should I track down this book at the library, a chore which will take up an hour of my precious time The principles of arithmetic, presented by a new method" in Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press: 83–97. Or will this pdf I found on the internet serve the same purpose? http://ocw.mit.edu/courses/linguist...pring-2004/lecture-notes/peano_arithmetic.pdf
Logic is not my particular area of expertise, but I imagine the level of understanding needed depends on where exactly your interests lie. There are large parts of mathematical logic that depend little on a deep knowledge of PA. Unless you have some prior grounding in logic some parts of that pdf will probably be rough going. It mentions connections to model theory and second-order logic at the end, and while it does not appear to require anything especially deep from either, some understanding will undoubtably be missed without it.
I already took a look at it. I keep putting the cart before the horse. I have three books on intro to proof theory and three books on intro to set theory. I'm going to read those first before I give mathematical logic a second shot because my first shot at mathematical logic resulted in failure.