How would you explain one of these theorems in the foundations of mathematics to a fellow colleague outside the field of logic (or rather to an undergraduate mathematics student) handwaving over the details?
The aforementioned link is by no means complete and following are some of the missing ones:
- Beth definability theorem
- Brouwer's fan theorem
- Craig interpolation theorem
- Mostowski collapse lemma
- Omitting types theorem
- Ramsey's theorem
- Shoenfield absoluteness theorem
- Tarski's undefinabilty theorem
- Vaught conjecture
- Well-ordering theorem
Due to the dearth of lucid papers on these topics -admittedly which is by no means easy to understand without pursuing years in college- my search has only yielded the following accounts:
- (The Cartoon Guide to) Löb's Theorem by Eliezer Yudkowsky
- Konig's infinity lemma
- Zorns Lemma (Axiom of Choice)
I am hoping to get a better understanding in expository terms of these logical theorems. Any reference that sheds light targeting students who had at most an introductory symbolic logic course at college level (such as myself) would be appreciated.
