Updated Introduction to Mathematical Logic

I’ve noticed that some of my posts that have gotten the most hits are my introductions to mathematical logic. Overall, I’m pretty happy with that series of posts, though I think since then I’ve come up with clearer and more precise ways of talking about the primary distinctions: syntax, semantics, and proof systems.

A little while ago, I gave a talk on the subject of “true but unprovable” statements. The goal of the talk was just to explore this notion and explain what exactly it means to a logician. In the course of developing the talk, I ended up re-summarizing the basics of mathematical logic. I think this summary makes a good “companion piece” to my earlier introductory series, as well as being more standard in its presentation. The most important slide is this one:

Here’s the link to the full slideshow: True but Unprovable

And here you can look through it on this blog (but some of the formatting got a little wacky in the embedding process).

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