Nonstandard proofs of standard results

I will give proofs of two well-known results: (1) the ordering of the natural numbers is minimal (the model theoretic notion of minimality will be explained), and (2) infinite Ramsey theorem for pairs. The proof of (1) is made particularly easy by considering an ordering of nonstandard natural numbers that admits automorphisms; for (2), moving the proof to a nonstandard extension of the natural numbers simplifies the standard argument somewhat, and gives additional information. The aim will be to fully explain all model-theoretic background for such proofs.

Roman Kossak